So the problem is that while rematch players change the color, looks like in first game you played white, on rematch you'd be black, and your opponent - evidently - white, but whites do have a privilege of kicking players who are joining their games.
Looks like we don't need "kick" button at all at rematch!
Yes this has happened to me as well. After the end of the second game the "guest," not the "host," seems to have gained the ability to kick. This kinda sucks when it's your table, and after you beat somebody they kick you from your own table!