Functions that make calls to external addresses are vulnerable to reentracy attacks.
Even though the CEI pattern is followed, which minimizez the risk, using a reentrancy guard will only add to the safety of the game contract.
The functions that may need additional safety:
withdrawFees
_finishGame
_handleTie
_cancelGame
Bad intended contracts can enter recursively and drain the game contract.
Loss of funds in the game contract.
Manual Code Review
Use a reentrancy guard modifier.
For example the one from OpenZeppelin: nonReentrant
For example in withdrawFees:
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