The really important issue here is not whether the policeman mistreated Gates per se, but whether he acted with a racial motive. So, even if he was wrong to arrest Gates, there remains the question of whether he did so for racial reasons. It’s quite possible that the policeman would have arrested anyone for contempt of cop, even if he shouldn’t have.
Now, it might be argued that the mistreatment per se question is still relevant — that showing mistreatment on account of race makes the showing of mistreatment necessary if not sufficient. That’s true, but I would add that, if Gates’s arrest was justified, yet a white person would not have been arrested, then the policeman’s behavior can still be criticized.