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This poor goes to the "game" described as a two person game. It isn't. The player who starts with white has the full control of the game and the player who starts with black is a poor bystander bound to be declared the loser by his opponent.

Why? White is in control of creating the first chain. He can deliberately wait until black is also ready to create a chain. Now the following goes on: White creates a chain, switches, black creates a chain, switches, white creates or modifies a chain, switches, and so on, until a checkmate is reached.

You can save the good ideas in this game by reformulating it as a puzzle or solitaire game (The solitaire player solves the puzzle, when he can reach checkmate with an unbroken chain of chains; otherwise he fails). To make the puzzle more interesting; vary the initial position (Fischer Random, Random pawn, both).

Reaching checkmate by a chain of chains may also be a nice fairy chess problem condition.