Honestly, they should take advantage of this as much as they can because next year they will not have Mbappe. I am sure that they can get a lot more players later on when the salary cap from Mbappe is wide open, which means that they could get someone great or a multiple great guys but still they would be closer. I think other teams may have slight chance next year, depends on the players they will get of course, if they get amazing players then maybe it won't be really needed anymore.
If you pay attention to the player spending table above, you can see that only Monaco, a team from Ligue 1 apart from PSG, is included in the top 20 list. This proves that PSG has everything to monopolize the League. They have money and can take any player by offering a very large contract. This will certainly make it difficult for other teams to find the players they need to beat PSG. If Mbappe officially leaves next season I think other teams still have no chance of beating PSG's dominance in the league. Unless other players can find talented players like hidden gems.