Theoretically, is the analysis of the moves more complex if the objective is to be the first to be checkmated? I have seen variations of other board games or strategy games where the aim is to actually 'lose' the game by forcing your opponents to make moves. Applying this concept to the rules of chess, would it require a completely different set of skills and thinking to let your opponent checkmate you first? Is the variation of moves and the analysis of the moves different if the winning objective or condition is reversed?
Although selfmate is a popular type of chess problems, the concept you have described simply would not work in a chess game played from the starting position; your opponent would need to cooperate with you if you want to get yourself mated. This means that any game played by chess players of any skill level would almost certainly end in a draw under your rules, which unfortunately makes your question moot.