The fact that you can't capture the king in FIDE chess is a *consequence* of the check rules, not a separate rule. Any move that would give your opponent the opportunity to capture your king is illegal; the issue of whether you're allowed to make the capture if you had the opportunity therefore never comes up, but the easiest way to explain the concept of check in the first place is by reference to the hypothetical capture of the king.
So, to recap, the laws of chess do not allow you to make a move that leaves your king 'in check'. If 'in check' means 'able to be captured by your opponent before YOUR next move', then when your opponent is about to get 2 consecutive moves, it would be illegal for you to make a move that results in a board position where your king could be captured within 2 opponent moves. Thus, players would need to foresee the capture 2 moves in advance just to check whether a particular move was legal.
It would still not be possible to actually capture the king, because every possible series of legal moves would result in the king being checkmated (and thus trigger the end of the game) before such a capture actually occurred. (Exactly as in FIDE Chess.)