And they really are guesses, because the nature of the industry is that one major hit can save a failing company overnight, while just a couple of expensive disasters can sink a successful company within a year.
EA probably have the potentia to be the highest-profile casualty. Despite their size and notoriety, they've not been doing brilliantly in financial terms for quite a few years now. They've a couple of nasty habits (from the point of view of both the gamer and the shareholder) which contribute to this.
The first is the continual chase after the "last big thing" - EA rarely comes up with new mega-hit formulas itself; rather, it belatedly notices when somebody else produces one, tries to mimic it and usually fails. Hence the expensive and largely unsuccessful attempts to copy the Call of Duty formula with Medal of Honor and Battlefield (the former in particular having been a costly disaster for the company) and the late arrival, whole-hearted embrace of and often embarrassing fiascos in the pay-to-win mobile space.
The second bad habit is that of making expensive acquisitions and then ruining their unique selling points. Bioware is the biggest example here; Dragon Age: Inquisition may do a bit of reputational-repair, but the Bioware brand is much tarnished from when EA acquired it.
EA isn't going to die overnight; if it does die in the next 10 years, it's more likely to be a "death by a thousand cuts" kind of affair, probably with some smaller rump of the company surviving. But despite the fact it has some really talented developers (it makes some amazingly good games, despite its reputation), I just don't think it's smart or agile enough to keep up with Activision, Ubisoft or Square-Enix in the longer term.
The funny thing about EA is that when it's gone, we'll probably miss it. It's used its (now slightly diminishing-returns) cash-cow sports franchises to fund some interesting games like Dead Space that would probably never have been made otherwise.
The next guess is, ironically, a company whose gaming division is doing very well and will likely continue to do very well right up to the point the company (possibly) collapses; Sony. Sony's currently building up the kind of console-wars installed-base lead it hasn't had since the PS2-era and is doing it with much healthier margins than it had during that generation. The problem is that the wider company is a shambles, selling electronic goods that nobody wants. There's still plenty of time for Sony to turn itself around, but it's not absolutely certain that it will.
Nintendo has perhaps the opposite problem; the part of the company that makes and sells consoles is doing pretty badly, while other bits of the business are doing quite well. The Wii-U has failed now. Aafter Mario Kart 8 and Smash Bros failed to have a significant impact on sales, it has run out of last chances and even Nintendo themselves seem increasingly reluctant to support it at the expense of the 3DS. It appears almost certain that the Xbox One overtook it on installed base somewhere around October/November, despite the Wii-U's 12 month head start. While the 3DS isn't doing too badly, it's more a "PSP-level" success than a "DS-level" success (though the PSP was indeed a successful machine) and is particularly dependant upon the Japanese market. I don't think Nintendo's going bust, but I suspect that the threat of a shareholder revolt may mean that the Wii-U ends up being the company's last home console (or they may try a panicked and quick-to-fail emergency successor, which will only slightly delay the inevitable). They have some strong brands though and if they can shed the home-console hardware business, they'll probably still be here and still be healthy in 10 years time.
And MS... will be discussed to death elsewhere in this thread. I don't think they're going out of business. I do think it's more uncertain that they will stay in the home console market, however. They've rescued the Xbox One fairly neatly after a disaster of a launch (it's had a good Christmas season in sales terms), but it is clearly never going to be the living-room dominance vehicle that their board thought it was going to be. Is MS interested in continuing to drive the Xbox brand itself on the understanding that it will only ever really be a games console, or will it seek a buyer? Dunno...
And then in the domain of the smaller developers, there are a few companies in obvious difficulty. Crytek are the most obvious; they've been out to commit suicide as quickly as possible over the last year or two and are already showing signs of distress. But there will be others too; the early years of a console cycle are often brutal for studios, as production costs rise sharply.
But I suspect the bulk of the failures are going to pass unnoticed. There's definitely a sense now that we've reached (and possibly passed) the peak of the indie-gaming boom of the last couple of years. I think a large number of the indie studios currently clogging up Kickstarter and Steam's Greenlight won't be around in 12 months time, let alone 10 years. A couple will probably survive, flourish and begin to look more like the traditional commercial developers - but the free-for-all we were seeing in 2012 is mostly behind us now.