You covered all of the main points. Here is my take on some of them.
The first thing that the internet impacted was gaming magazines. You could now lookup a walkthrough online, and walkthroughs and hints were the biggest reason people bought gaming magazines. Also the internet had a very immediate impact upon Adventure games as a genre, because online walkthroughs destroyed Adventure games. This may have had a bigger impact than you might think. In the 90's the games with the best stories were Adventure games (although RPGs were somewhat competitive on this.) Before the internet, when a developer wanted to make a story oriented game, they would make an Adventure game. It was kind of a way to be an interactive novel, but it very much relied on the puzzles taking some time in order to be solved. After Adventure games died off as a genre, you start seeing narratives in almost every type of game. I would argue that a heavy narrative works a lot better in an Adventure game than it does an action game, since when a person is playing an action game they just want to kick some ass and the story is kind of a distraction to that. But, because Adventure games died off, we get narratives in most of our action games now.
I agree that the internet had no impact on American arcades, since they were killed mostly by consoles. Specifically most developers decided to focus on console games, because it was much easier to make money on the NES and SNES than on an arcade machine. The lack of developers lead to a lack of arcade games and it inevitably declined and died out.
On the PC side, there were a lot of changes going on in the 90's and early 21st century. Some of these were impacted by the internet and some were not. One thing impacting PC's were that a lot of action games that started on PC's were moving to consoles. This sort of thing actually happened with EA first, when they moved most of their titles to the Genesis. When Sony came around it happened more, with franchises like Tomb Raider and GTA moving from the PC to a console. How much impact did this have on the PC? In my opinion, not much. Action games tend to be a better fit on a console. When I look at the best selling PC games in the 90s they tend to be things like Myst, Civilization, Rollercoaster Tycoon, and several games made by Blizzard. Add in The Sims from early 2000 and you see what kinds of games were popular on the PC: Adventure, Strategy, Simulation, and (to a lesser extent) RPG. None of these are action games. So I think the PC would have still been fine even with action games going to console, because the best selling PC games were not action games at the time. Without the internet, the PC would have been the main place to go for Adventure, Strategy and Simulation games and to a lesser extent RPGs.
So, two PC genres that were affected hugely by the internet were MMOs and FPS games. MMOs would simply never exist. FPS, on the other hand, is probably the only type of action game that actually is important to the PC, and I think its safe to say that FPS multiplayer is the main draw for this type of game. In the late 90's, laptops were not nearly as ubiquitous as they are today. I tend to think that as laptops became more popular, then LAN parties would have become more popular as well. In the absence of the internet, this may have made PC gaming a solid home for FPS games. After all, the PS2 had FPS games, but the FPS genre never really had serious sales numbers until generation 7 when online gaming came into play. So, in the absence of the internet, I think LAN parties become the norm for FPS games and the genre tends to remain dominant on the PC.
All of this means that the PC would not undergo radical changes. PC gaming would continue largely as it had before and it would continue to have a retail presence. This is both good and bad. For places like the US and the UK, PC gaming would continue as strong as it always had. But one advantage Steam has had is that it has made PC gaming accessible to places where gaming doesn't have a strong retail presence. I suspect there are a lot of places in the world like Russia, India, etc... that would not have much access to gaming if it had not been for Steam and online PC gaming.
Lastly, there are consoles. I actually think digital distribution has had an even bigger impact on consoles than even online gaming. First of all, there would be no smart phones without the internet. Handheld systems have probably lost some sales to smartphones, so without the internet, the handheld market would be at least as strong as the home console market. On top of that the "indie renaissance"would have happened on handheld devices, since that would be the medium where game development would have been the cheapest. I also think that games would be less likely to ship early in the absence of the internet. There would be a bigger effort to get it right before the game ships out the door once and for all. I also think Gamestop and similar stores would be in much better shape without the internet.
Tying it all together, I tend to think today's gaming scene would resemble the 90's gaming scene a lot more without the internet. Gaming magazines would still be ubiquitous. PC gaming would still focus on non action genres like Adventure, Strategy and Simulation. PC gaming would continue to have a retail presence and gaming stores would continue to be thriving. In the absence of the internet, LAN gaming and handheld gaming would take the place of internet multiplayer and smartphone games respectively. In general, gaming would continue much closer to the trajectory set during the 90's before the internet came in and changed the gaming landscape.
Regarding FPS games, the genre was already showing signs that it was viable on consoles in the 90s. On the N64, GoldenEye 007 sold 8 million copies, Perfect Dark sold 2.5M despite coming in near the end of the system's life, and both Turok 1 & 2 sold over 1M a piece. In Gen 6, Halo CE sold 5M copies despite not being an online title. Halo 2 sold over 8.4M, though it's uncertain how much of its sales improvement over its predecessor was due to the online; it generated record-setting pre-orders and had the biggest debut of any game ever at that point at a time when Xbox Live had a very low adoption rate relative to the install base, though the growth of XBL subscriptions from 1M in July 2004 to 2M by July 2005 can in most part almost certainly be chalked up to Halo 2. Aside from Halo, the Xbox also had other modest hit FPS titles: its port of Counter-Strike sold 1.5M copies, CoD2: Big Red One sold nearly 1.4M, and Ghost Recon sold over 1.1M. Additionally, both Star Wars: Battlefront games sold over 3M copies between the PS2 and Xbox, and the PS2 versions of Medal of Honor: Frontline and MoH: Rising Sun were multi-million sellers as well.
Meanwhile, on PC most notable FPS titles weren't actually massive hits. Looking at games released in the period of 1997-2007, by far the biggest blockbuster hits on PC were Half-Life and Half-Life 2, both selling 9 million copies. Counter-Strike sold something like 4M copies. Meanwhile, titles like Quake II, Unreal & Unreal Tournament, Battlefield 1942 & BF: Vietnam, and Far Cry performed relatively modestly. The last legitimate hit PC-oriented FPS was Crysis. And several notable PC FPS titles owed their success to online multiplayer, namely Quake III, Unreal Tournament, and Counter-Strike.
So, even in the early to mid 00s, FPS games were at least as popular on consoles as they were on PC. In a world where the internet never existed, I don't think it's too far-fetched to think that they'd have continued to be popular on consoles. By the start of Gen 7, they had already demonstrated their commercial viability on consoles. I imagine Halo still would have done well for itself. Call of Duty and Battlefield would almost certainly be a lot less popular, but they would probably still be around. The genre as a whole would be primarily single-player experiences, with some perhaps still having a split-screen competitive mode as well (though again I wonder if the LAN would have still been a thing). Many if not perhaps most FPS games would still come to PC, though, but I doubt the genre would have ever remained predominately PC-oriented. The cracks were already beginning to show in the late 90s, and in the decade between Quake II and Crysis there were only two smash hits that were single-player focused (both Half-Life games). There were only a relative handful of others that pulled over a million copies, but they were eclipsed by the big console FPS titles in overall popularity. If we were to make a Top 10 best-seller list of FPS games released after the launch of the N64 but before the launch of the 360, while the top two spots would be held by the Half-Life games, the rest of the list would be dominated by console-only titles and multiplatform titles that owed most of their success to their console versions.