Business will continue as usual. Sony gained absolutely nothing from having those stocks, thus there's nothing to lose by selling them. They are bleeding money right now, so they cannot afford investments that don't exactly generate any profit. Square Enix on the other hand won't survive without Sony (that is, unless they want to become a full-time mobile game company). The vast majority of their best-selling games are tied to the PlayStation brand.
According to reports, the Final Fantasy XIII games have a sales ratio of 4:1 between the two available formats, in favour of the PlayStation 3. And it should go without saying that the Xbox brand is dead in Japan, so all of their AAA games are de facto Sony exclusives over there. There is definitely profit to be made from releasing games like Final Fantasy XV and Kingdom Hearts III for the Xbox One here in the West, even though these games will still sell better on PlayStation 4. But given that Square Enix is a Japanese company, Japan is their main market. As such, it would be a fair assumption to say that these games are developed with the PlayStation 4 in mind. The Xbox One versions will most likely be treated as ports for the Western market (and quite possibly even be outsourced).
Square Enix have a great relationship with Sony Computer Entertainment. Like you mentioned in the article, they also have a good relationship with their parent company, who basically helped keeping them afloat until the merger with Enix. Without either Sony or Enix, Square would not have existed today. They would have no problem understanding that Sony, the parent company, is now in financial trouble and can no longer afford luxuries such as owning shares in companies that don't generate a massive profit for them.
But even if you ignore the financial aspect, what good has come out of owning those stocks in recent years? Nothing. The only IP from Square Enix that has remained Sony exclusive is Drakengard, yet the third game almost didn't make it outside of Japan because it's fanbase is so small. Porting it to Xbox 360 would have been a bad investment unless it had been bundled with HD remasters of the first two games.
Whereas Final Fantasy X/X-2 HD Remaster remains a Sony exclusive, that is more than likely the case for the very same reason. People who like Final Fantasy are primarily PlayStation customers. They would also have to spend time, effort and money on porting these games, originally developed with PlayStation technology in mind, to a non-PlayStation platform. We're probably talking about 200,000 sold copies on non-PlayStation platforms tops since these aren't new games. Not a good investment. The same can be said about Kingdom Hearts, although I do think that if the Wii U hadn't bombed so badly they would probably have made an effort to release the HD collections on that console as well.
Yes, A Realm Reborn is sort of Sony exclusive, since PC generally doesn't compete with consoles. But that is only because Microsoft has a ridiculously childish policy about cross-platform play (they literally don't want Xbox players to be able to play on the same servers as PlayStation players). Square Enix have also expressed how difficult it was to get Microsoft to make changes so that XI could be released on an Xbox console. If they could warp back in time, I am dead certain they would rather have offered to port XI to the PlayStation 3.
And while Sony haven't really had any proper exclusives from Square Enix, Nintendo certainly has enjoyed some support on the 3DS! Why Theatrhythm hasn't been ported to the Vita is beyond me. Seems like a perfect match. But more importantly, Bravely Default is a system seller. Square Enix never gave Sony anything like that in recent years. The Vita got the HD Remaster of X/X-2, but really, that was only because it was easy to port it from the PS3 version (which is obviously the main edition).