No, you couldn’t play because it wasn’t your turn, they requested the undo on their turn. You can never make a move on an opponent’s turn even if they request an undo.
There were some visual bugs / oversights which meant it wasn’t visually clear that it was your opponents turn, but the bug was not that you couldn’t play. If you read some of the above posts they talk about how the text “White to move” was missing, a slight glow around one of the player cards was missing, and there was no last turn symbol on the board.
Games are not annulled just because an opponent timed out. For it to trigger you need more than one timeout in a row, and it is also not annulled if the person was likely to lose.