This game is a 7up-licensed version of an Othello-like board game called Ataxx/Infection.
This is the fastest solution I could find. I start off with the bottom right corner because the AI doesn't move the way I want him to if I start with the closer tile first.
Noxxa: This is another run of a board game where the gameplay is not meaningfully changed from regular play, and depends again on bad decisions by the AI to be defeated as fast as possible. Additionally, the animations can be disabled, which would speed up the overall game by quite a bit, which means the run is suboptimal in time too. As a potential speed-entertainment tradeoff, the animations do not do enough to keep the run afloat. Rejecting.