This market is probably too lucrative to ignore.
May well end up forcing Sony to do likewise. Now with that being said Microsoft with its lateral into this market. Then for them the obvious answer should be to have the service lag behind their console by say eighteen months to a couple years. They would be going out of business right now, and as Sony is not likely to offer up new service specific games. Were Netflix or Hulu to only offer up shows from four or five years ago. Sony as a company can be incredibly stupid and shortsighted, but I seriously doubt that they will not take note of what it is that other streaming services are doing. Let alone one worthy of paying a monthly subscription for. Not if they intend to continue to offer their streaming service as a viable option. It is just really hard to see them holding out until their next console launches to release games for their current generation console onto the service. It not being a major franchise, or a console seller as it were. As such this title would be a prime candidate. Sooner rather then later current console generation titles will have to start trickling onto the platform.
They expended considerable capitol in acquiring the service, and a major part of maintaining it as an ongoing concern is updating their inventory. There is a very high likelihood that we will see this title being made available through their streaming service by around years end.