My belief is that Nintendo and the NES didn't save gaming, but they did prevent the market from being set back a decade.
In the mid-80's, you had three main regions (USA, Japan, and Europe) and three main pillars (Arcades first, followed by consoles, and PC in distant last place). The question of "Did Nintendo save gaming with the NES?" implies that all three pillars in all three regions would have either been extinguished or otherwise would have remained stagnant indefinitely.
In the arcades, I don't think that gaming as a whole was in true mortal peril. On the arcade front, big games continued to be released during the mid-80's. 1983 had Donkey Kong 3 and Mario Bros, 1984 had Space Ace and Marble Madness, 1985 had Paperboy, Hang-On, and Gauntlet, 1986 had Out Run and Gauntlet II, and 1987 had Blasteroids and RBI Baseball. None of these games sold as well as Donkey Kong or Pac-Man, but they were games that sold thousands of cabinets, from different developers located in different countries. Arcade gaming never fully recover after the Crash of 1983, but it did stabilize even before the NES hit its stride in the West.
Next up, we have to address other console manufacturers. In short, I have little doubt that another manufacturer besides Nintendo could have filled a similar role, at least in Japan. The SG-1000 came out the same day as the Famicom and despite strong competition, did well enough for Sega to follow it up with the Master System. The Sega Master System, though widely considered a dud, ultimately sold over 17 million units worldwide, though most of that was outside Japan and the USA. The PC Engine would have likely released off of the success Hudson had on platforms besides the NES. And bear in mind that the 3rd party support that Nintendo largely monopolized in real life would have been on Sega and Hudson consoles.
As for Europe, what about Nintendo? The NES barely outsold the Master System there, and the Genesis outsold the SNES. And of course, PC gaming owes little to Nintendo, besides being indirectly responsible for a wave of sidescrollers in the 80's and 90's.
THAT BEING SAID:
Even if every third party game sold just as well on other hardware as on the NES, it doesn't change the fact that Nintendo was the lead creator of software by far. On the Famicom in Japan, 23 of the 43 million-sellers on NES were 1st or 2nd party games, including 16 of the Top 20 sellers. Games like Bomberman, Lode Runner, and Star Soldier might have sold a million copies on the Sega Master System or some other hypothetical 8-bit hardware, but they wouldn't have reached the heights of Mario or Dragon Quest. And speaking of Dragon Quest, that series could not have grown to the extent it did without a massively popular platform to support it, so don't expect the JRPG to become as big a deal in this timeline, even if it does migrate to some other console.
Without Nintendo's games to drive hardware sales, it is unlikely that third party hits would be able to sell as well, even continuing into the 4th generation of gaming. Companies like Sega, Hudson, and SNK would be fine, being the primary hardware makers in Nintendo's place, but other companies would have to rely more heavily on arcade games, and even those arcade games wouldn't sell as many home console ports. So companies that did much of their work on consoles like like Squaresoft, Enix, Bandai, etc? All are going to be a lot smaller. And even arcade juggernauts like Capcom would have less cash in their pockets. Because really, how would they have sold the 6.3 million copies of Street Fighter II that were sold on the SNES?
Which brings us to more modern times. Why would Sony ever make a console in this environment? Even if someone else made the same mistakes Nintendo did, would such a small market be worth the investment? Later, why would Microsoft make the Xbox without the looming PlayStation menace.
In a world where Nintendo never releases the NES, and instead sticks to being a third party and MAYBE releasing a handheld, I imagine the console market worldwide would be half of it's real life size in the late 90's, and maybe to this day. I figure that after the 90's, a lot of PC developers would go broke without the ability to also release their games on highly popular consoles to make some extra money. Digital Distribution would help PC development eventually, but only after more developers are killed by the niche size of their markets.
Conclusion: The NES didn't save gaming, but it did more good for it than any console ever since. Which is close enough so that I can see why people say it saved gaming.
Love and tolerate.
