That's tough. Unfortunately mesh wifi will add latency as you're adding hops inbetween you and your router. I haven't used any of the new mesh networking gear, so can't add much on the gaming front.

Might pay to get a quote for a couple of ethernet runs from a data cabling company, just to see how it compares to buying a higher end mesh system. You might get away with a single AP for each floor for less. For comparison ours is an older UAP-HD which is only 802.11ac but covers pretty much all our 160m2 house, but we're not concrete block.