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This is software coming from a server, not hardware. It doesn't matter which device it's run on, or whether it's in your home or not.

You are not entitled to play the game, which is hosted on their server which requires bandwidth and other resources. In the same way that you are free to make demands about how software runs on your machine, the author is free to make demands about the use of their software.

If the data gathered is only on gameplay, and not something that can be used as PII like IP addresses or device information, then it should be fine. Gathering things like the score and time spent completing the level, isn't a problem. This could be used to rank the levels, without gathering any user information.

If gathering the data should be fine, then asking for permission should also be fine.