Mesh is still wifi and it suffers all the same problems as wifi. Key is interference causes date retransmissions which causes random delays. If you are not a online gamer you will not even notice. Gamers will see lag in games because of it.
Now adding mesh especially if you are actually using the "mesh" feature means you have multiple wifi jumps. Each can get data corruption. So now you have multiple sources of lag for your game.
So even if it is a pain I would still fix or rerun the cable. After that you try powerline networks or maybe Moca if you have tv coax. Then you would try wifi and very very very last you would use mesh repeaters.