You lost me on that complaint. I suppose I see the semantic nuance you're going after, but it's firmly established as an alternate usage for the word "beat" in the parlance of our times. It's like trying to wage the war against ending sentances with prepositions. Sure you can argue about it being grammatically incorrect, but so many people do it because it's less cumbersome and so many figures of speech use it that it's not really worth spending much time on it.
Additionally, I feel that beat is basically a synonym for defeat in this case and there is a sense of victory when I finish a game. It's not quite as directly applicable as if I had some form of finite opponent, but the meaning is clear.
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