Are engine ratings directly comparable to human-level play? Yesterday, I play a game against Stockfish 7, and it has 2200 rating points.

I drew 2 games, and lost 1. The point is that if I play against a human-rated 2200 player, I would probably have a positive score against him.

I also noticed that Stockfish 7 played much better than the average 2200 human player strength.

Do human-ratings and machine-ratings show the same strength of play?
What you have to understand is, first, that any rating is just a comparison of players within that pool. So a 2200 on chess.com is not the same as 2200 on lichess.com, or on ICC. They are probably close, but it is not the same.

Second, you need to realize that your three game sample is just not enough to draw any valid conclusions. You are human, so even if your winning expectancy were .95, you can always defy expectations, and make a blunder, and the computer, even handicapped, would still likely take advantage of it.

Lastly, at 2200, you are playing a handicapped computer. It is playing "not best" moves, but how is it playing them? Is it being told to play the fourth best move every time, or is it being told to play the best moves every time, but on the 5th move, play the 10th best move? Either way, you could have an anomaly where it plays less bad moves in an individual game, and when those worse moves do pop up, maybe you miss the opportunity.

The computer can only be handicapped so much.