Are both sentences OK?
A player just got hurt.
If I say;
It appears that he might not be able to continue the game.
There is a possibiltiy that he might not be able to continue the game.

Question

Answer

Both are correct.  If you say this:  "It appears that he might not be able to continue the game."  It means that the player is NOT expected to be able to continue the game.

If you say this (fixed spelling error possibility): "There is a possibility that he might not be able to continue the game." It means that you are unsure if the player will be able to continue the game.  Maybe yes, maybe no.

Answer

Both are correct.