I have recently been playing a lot of games against the Computer level 9 on chess.com(not to be confused with Komodo 9). It is actually a reasonably difficult computer I would say rated definitely over 2200. I have been taking the King's Indian approach quite often due to the closed center it establishes and the strategic ideas that are brought into the position. The computer makes mindless moves since it doesn't have any plan and it underestimates
Computers have a few advantages over us: speed, memory, and they don't make mistakes (based off the code they're written on). This allows them to go very far ahead in the search tree, navigating the tree perfectly. However, with an engine you estimate to be around 2200, you may have advantages in position evaluation and intuition.
With this in mind, there are a few things you can do:
1) Aim for positions where a high search speed isn't as important. Closed positions are ideal, as you mentioned.
2) Try to drive the game towards positions that you feel comfortable evaluating. An engine rated only 2200 may have an advantage in a concrete tactical position, despite its vastly reduced search depth compared to an engine like Stockfish. But in a positional structure you have experience with, you may have the advantage.
3) Don't go too far out of your way to play differently though. If you get carried away with this, you'll only be playing the opponent and not the game. One reason Kasparov ran into trouble against Deep Blue was that he figured a computer wouldn't make a calculation mistake. If you yourself are around 2000-2200, you already have a decent chance of scoring against a 2200 player.
Even if you want to beat a computer, if it out-rates you by a lot, expect to lose a lot more than you win. If it out-rates you by enough, you still might not win at all.
While you definitely want closed positions, I do not know that the King's Indian will do that enough since there are too many ways to open the position up.
My main suggestion is to study the games of Hikaru Nakamura versus computers. He used to play on ICC versus computers A LOT, and he was probably the most successful player I have ever seen play computers. I would emulate his openings, and go from there.