I can respond to your post further, after some thought. Foremost I am not sure your questions should be answered without first establishing if "bearcat skilled play" (BSP) is identical to "skilled play" (SP). The view I will put forward is that it is not.

The conception is problematic: it contains significant omissions. We should consider when the win conditions are not defined, or arbitrary, or defined after the fact, or there are a plethora of them. We should also look at moves that are considered more skilful even when they do not take us any closer to the win condition, and moves that are not considered skilful - gimmes let's call them - even when they take us closer to the win condition.

Taking your example,

- I have available the moves -2, 4, 13. I don't know the win condition and choose 13. Was that skilful?
- I have two win conditions - get to 30, get to -30 - is the only unskilful move picking 4?
- I have another axis in play - to choose a number I must first overcome a challenge on this second axis - is choosing 13 now more skilful than it was in your example?
- I choose 4, and convince everyone my win condition was get closest to 5. Which was skilful, choosing 4 or convincing everyone to accept my win condition? Both? Was this then more skilful than choosing 13 in your example?
- I am offered -2 and 4, and you are offered 13. I choose 4 and you choose 13. Given the win condition in your example, did you play more skillfully than I? You certainly got closer to the win con, right?
- I am offered 13 or 13, but to select the former 13 requires I recite Feynman's Lectures from memory, giving insight into his understanding of quantum mechanics. Is it more skilful to select the first 13, or is it the same as selecting the second, given both carry us the same distance toward the win condition?

I'll stop there, not because there are not more cases, but because I believe we would need to say more about win conditions and dimensions of challenge in play, and the factors players engage in overcoming them, to develop a satisfying conception of skilled play (and I contend, that would still not necessarily count as "skilled play" which can be played without skill).

a) One can play skilfully,

*without* approaching a win condition. b) The ability to play skilfully can help toward achieving a win condition. c) There may be skilful moves available - acts that all observers will agree are skilful - that have nothing to do with any given win condition. d) Some moves may be more skilful than others, along axes in directions other than the win condition.

The acceptance of win conditions, and exercise of skill in play, are not intrinsically linked as you put it.