That has happened to me to, but only certain games show that. When i hover over the play it also says I am playing myself
Game shows that it is my move when it is the opponent's turn to move

Several other threads mention this -- It's happening to me too.
(example: https://www.chess.com/forum/view/help-support/i-am-playing-myself)
A daily match shows that it is my move but it is my opponents turn.
This game appears under "My Turn" list when I hover of the move icon (hand moving piece) in the left tool bar.