The X1 version already is a 1080p version :p

The definitive edition will have 1081p at least.

I don't know, I think there is a good chance Sony decides to teach SE a lesson by letting TR limp out to die.

Don't think so. They don't care for this.

It depends on Square. If they come to Sony with a "Rise of the Tomb Raider: Omega X Definitive Gold Edition" then I think they might get some love. Game companies like to brag about how their edition is miles superior, so much the better if it's true. It's a feather in the cap.

As for teaching Square a lesson, I don't believe that. These are businesses who are always looking to increase their position in the market. They might make Square work a bit harder but it would end with that. The market itself has already delivered a lesson. None of this is personal.

relaunch? when did it launch the first time?!..

Does it matter? Sony has FF7 Remake. That makes Tomb Raider irrelevant in comparison. Actually, it's not even a comparison.

Relaunch? I wouldn't be surprised if they saved Horizon for the exact same day as it launches. Its one chance was to launch in the quieter May-July months, but no they want to bring it out next November, so good luck with that.

I doubt it's going to take all the way to the Fall of 2016 to come out, wouldn't be surprised if it comes out at the same time as the PC version, with the game having further improvements on both due to future updates in API and improvements to Square's rendering tech.

I could see it running at 60FPS on PS4, with better AA and other visual improvements, we'll see what happens though, likely hear about this a month or so into the new year.
IMO Square's best bet would be to launch it months away from Uncharted 4 and Horizon Zero Dawn, because RTR will get curb stomped by both IMO.

Don't think they will, or should. o.O Don't get me wrong, timed exclusivity, like all other exclusivity deals, are the typical things that publishers and platform holders will do, but if a Publisher choose to release their title a year earlier on the competitor's platform, I (by which I mean as a platform holder like Sony or Microsoft) wouldn't be gung-ho to throw any of my advetising money at them once that year was up. I mean... what's the point? =P Chances are people eager enough to buy a console specifically for Tomb Raider will already have bought an Xbox One, meaning they'll have already gotten the part of the market to which that game would have moved units, whatever size the market is. Those who specifically choose to wait a year to get it on PS4 either already have owned a PS4 or are going to get one in the next year regardless of how enthusiastically it's advertised.

The only beneficieries to Sony throwing marketing money behind Tomb Raider would be Square Enix... sure, great for Square, but these marketing deals are supposed to be about mutual benefit. There's no benefit to Sony in spending money on this. =P Far better to earmark those funds for, at the very least, a title that will be arriving on both consoles at the same time.

The only real exception I can think of is if Sony works out a deal that doesn't solely extend to Tomb Raider, i.e. 'Sure, we'll market your game's release on our platform! But about that Final Fantasy 7 Remake exclusivity period... how bout we add on another few months, eh?' Using Rise of the Tomb Raider marketing as leverage to gain concessions on other fronts could be beneficial.

Although one thing to note is that, depending on how much funding Microsoft provided Square, the actual sales figures needed for Square to break even/make profit might be significantly lower than it was for the first Tomb Raider title. =P More of a financial cushion might have them satisfied, even if not exactly thrilled, with these initial sales.