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A most interesting concept.

Thank you! Here is a test game https://www.chessvariants.com/play/pbm/play.php?game=Jabberwocky+Chess&log=pokshtya-cvgameroom-2024-275-280

The final position in this game is Jabberwocky Mate - The Black King cannot capture the White Rook because then Black would be left without a king.

This looked like a great chess variant and got excited about it until I reached the rule saying "Capture is mandatory", which changed this great idea into a different version of "Antichess". 

I wouldn't say that every game that has manditory capture is an 'anti-game'. International Draughts (and I suppose also Checkers) has an anti form where you win by getting stalemated (usually because you lost all your pieces, so you have nothing to move). But both the anti form and normal Draughts have mandatory capture.

So it seems the winning condition is more important for defining the character of the game than whether capture is mandatory or not. Of course mandatory capture is essential for winning by getting stalemated, as it would otherwise be impossible for a player that is so weak that he can be stalemated at all to force the strong player to do that. The characteristic of anti-games is that the means defeat the purpose.

BTW, it might be counter-intuitive, but pieces in Suicide Chess do have positive values, albeit somewhat different from classical values (e.g. e Queen seems to be worth 6 Pawns). If one of the players would start with his Queen removed he would lose very much more often than not.

The "Capture is mandatory" rule was introduced after several test games. Without this rule, the game could go on forever since the usual concept of a checkmate is absent and the cycle of transformation of pieces is closed. However, nothing prevents you from playing without this rule.