Hmm...processing power is easy. Human input is slow. Unless the mystery team has (1) determined what real-time inputs really matter, and (2) has installed sensors that detect those inputs, then this Cray thing sounds like a story meant for release on April 1.
There are about a half-dozen other questions this story should provoke: some team developed a real-time stat system without another team knowing? Who wrote the software, in secret? Is it portable? If not, then what does the team do on the road? If the manager comes to depend on The System, aren't they something like a modern "developer" forced to write a system in assembly language?
OK. I'll now return to my regularly scheduled job as a semi-retired computer programmer.
With the cameras they've got in parks these days, it shouldn't be too hard to get a real time analysis of things like pitch break, etc. You can also very quickly note things like how often the catcher calls for it low and in when the count is 1-2 and have the machine start noting those patterns. Yes, you can do it with pen and paper but it's easier with a computer. Assuming you have something like a quick form that tracks things like count, infield in, guarding the baselines, shift, whatever, and toss in how fast the pitcher is to the plate from the windup, the stretch, etc., you could probably put together a pretty impressive probability spread. A computer that fast means they're getting automated input with a LOT of data. Again, that means likely they're scanning video feed and pulling data out of it.
Given the foray into drones, I could see a video stream being analyzed for positioning of the players, depth, etc and some sort of database being built up around that. As for away games, I don't see why you couldn't take the same video feed and run it over a decent broadband connection back to home base. Given RDP and modern bandwidth, this shouldn't be even remotely a problem.
Granted, video analysis like this isn't my field of expertise (networking, tunnels between sites, etc. is) but I'm pretty sure that anything that doesn't involve video wouldn't need a Cray. That kind of power means realtime analysis of a huge chunk of data.