If my elderly parent damages my home and then pays for it, will it be considered a gift for Medicaid purposes?

If he has dementia to that extent the parent may not be able to agree to reimburse for damages, especially if there is no rental agreement. Consult attorney well experienced in Medicaid and review power of attorney agreement if that is what you are basing intent to get repaid. If you are just repaying self without POA or guardianship, you may have a problem.

I hope he realizes he can't continue this behaviour at the AL. Doing this there will not be tolerated. For one thing the residents have a right to a clean environment and a sanitary environment.

I agree with Alva. At least a contract saying that because damage was made by him, he is reimbursing you so the floors can be replaced. But, it would not hurt to run it by a Medicaid caseworker or an elder lawyer.

You need to pass this one past an elder law attorney. There would need to be a clear contract I would think, for exactly what damages, how many assessments for replacement, and etc. This is, I am assuming, in YOUR home. If there is a clear rental agreement with damages clause, then you are OK. But just Mom writing out a check for new flooring is very likely to be questioned I would think.
Cover your bases as this isn't something you can afford to guess wrong about.