The egg headed literal answer is follow Figure 8.6.5.1.2(b) or whatever figure it is in the applicable version of NFPA 13 (the obstructions against walls figure). You are dealing with an obstruction to discharge issue.
The sprinkler head is so high up there is obviously no way it will throw water diagonally into the alcove.. Hence the 2-ft of floor area will be unprotected space using strict interpretation of 13.
That said it is so small of an area, if an AHJ questioned you on it I would be highly surprised. This is one of those things I might notice as technically being out of conformance and say, "huh interesting"..but would not comment on, ever. I have learned to pick my battles, there are plenty enough of them, and it is obvious this is a non-issue even if the standard doesn't say so..
Sure, they might fill that alcove up floor to ceiling with a rack of foam dodgeballs, which ignite.. but so what. That might not even develop into a fire large enough to pop a head in the gym since the ceiling is so high. If it did, the sprinkler(s) would contain the fire to within the alcove, and might even splash enough to wet the alcove enough to suppress the fire.
I would drive on and not worry.
Real world knowledge doesn't fall out of the sky on a parachute, but rather is gained in small increments during moments of panic or curiosity.