Depends on the game and your expectations of details.
I play Starwars: the Old Republic. For single player, there's no worries at 1080p, game capped at 90fps ultra settings on a i7-3770k @ 4.6GHz and gtx970 OC 128%. 8man team is no issues there either, still above 60fps. 16man and fights get laggy with the sheer overload of AI and post processing, have to drop to medium low, and it's still glitchy in some massive fights. 24man boss fights are almost non playable. There are definite drops to 5-10fps at lowest possible settings, average fps is 15-20. It jerks constantly when bouncing in/out that last 500Mb on that card.
And that's a 7 year old game. Any multi-player game will be similar, all the benchmarks you find are single player where fps is usually cpu limited on the bigger cards. So the really intense multi-player games are going to be brutal, a lot more so than any single player bench will show.
A 2070 overkill for 1080p? Not really at all. There's many times when even 1080p can tax a 2080ti. It's all dependent on the game.