In a "friendly" blitz game I got into an argument with my opponent in the following scenario:
My opponent's knight was pinned to his king. He did not notice and touched his knight to move it. I became excited and before he had a chance to press his clock, I took his king.
The question is: by official rules does my opponent lose the instant he touches the knight? (Making any action taken after this instant irrelevant?) Or does he need to "complete" the move by pressing the clock?
The touch-move rule never compels you to make an illegal move. It may compel you to make a stupid move, but not an illegal one. For example, you'd be forced to move a knight that's pinned against your queen and lose your queen as a result, but you'll never be compelled to move an absolutely pinned knight which would put you in check.
See this related question for more discussion, but I'll quote here the relevant FIDE rule here:
4.5 If none of the pieces touched in accordance with Article 4.3 or Article 4.4 can be moved or captured, the player may make any legal move
Taking the king is not a chess move, and putting your king en prise is an illegal move.
I wish your rule was the rule. I could draw with Magnus Carlsen every time. I would touch my rook on my first rule, and as I have to move it and can't, therefore, I would walk away with a draw :-)
Touching a piece that cannot be moved such as the rook in my case, or the knight in your case, simply results in the touch being ignored.
So in your case, you were mistaken: he simply needs to make a legal move with any piece and then press the clock. I believe had he completed the illegal move, you could have asked him to take it back, and get a time bonus in blitz.
However, touching the knight does not compel him to make that illegal move.
If your opponent moved his knight and let go off the knight then he has made his move and you may reply before he presses the clock. If you wait until he presses the clock then you can claim that he made an illegal move. The penalty for this in blitz is that you get an extra minute on the clock, the position goes back to before his illegal move and he has to make a legal move. If he completes (i.e. makes and then presses the clock) a second illegal move then he loses the game.
But instead of letting him press his clock and then claiming illegal move you took his king. First of all once you make a move you lose the right to claim for your opponent's illegal move. Second, taking the opponent's king is also an illegal move. If you didn't press your clock then you can take back your illegal move and make a legal one. If you took your opponent's king and then pressed the clock then your opponent can claim illegal move and gain an extra minute on the clock and the game continues.
Bottom line, your opponent does not lose because he made one illegal move. He doesn't get punished unless he completes the illegal move and in blitz you must claim for the illegal move (or the arbiter must see it and intervene) otherwise the game continues. Taking the opponent's king is also an illegal move.
Note that these are the rules for blitz and rapid. The rules for standard time controls are different.
In this scenario you are the one who loses (in case tournament regulations specify that an illegal move results in an immediate loss), not your opponent. As you stated in the question, your opponent has touched their knight and while moving it, you captured their king. Provided your opponent has not pressed their clock, it is their turn, not yours. Thus, you made a move in your opponent's turn.
As @itub stated, the relevant line from the rulebook clearly indicates your opponent has not made their move (as the knight move they intended, but not played, does not count).
