i lowkey forgot the plot of this story bcs recent chapters pmo ( ̄へ ̄)
and to answer your question, no, i don't think they're childish.
the uke is extremely territorial (to seme only), ego-driven and has an inferiority complex towards the seme. meanwhile, the seme is the texbook definition of dismissive-avoidant. he's extremely charming, emotionally detached, and highly observant.
they both love playing mind games, the seme usually wins because uke just can't let go of his ego lol
they're perfect match made in heaven bcs they're both possesive of each other. also, they are both dominant, so they don't have a time to act childish, it's just the uke is insufferable bcs of his inferiority issues lolll. but don't worry it gets better. you can check it out now that it's already completed!! istg I can't count how many times i reread this.
https://www.mangago.me/read-manga/checkmate_1/

they remind me of checkmate so much