I wonder if this is setting up Nitanda to be the one who has to step forward and be the aggressive one in any future romance narrative between them.
Machino is clearly flustered this chapter, more overtly than any other (in terms of actual panels/pages where she's caught blushing/doing her "hrrmmm" face of embarrassment where Nitanda can't see it).
Because she's the aggressive/forward one between them (literally coming to him every chapter being the physical precedent) and he's the reactive Straight Man to her antics, they have a clear, established relationship of her being the pursuer and him being the target - from the way they meet up, to their conversation exchanges, to the way she's the one who's pushed him each time to go and do something outside of dominoes (the dance video, the afterparty, the Maid Hunt).
Machino's comments about him being the passive type, explicitly stating it in this chapter only for him to show that he'd actually taken the initiative for her birthday without knowing when it would be, is a flip on the script of their dynamic, and I believe the first one for them, as well. Doubling the fact that it comes off the back of her being put out by him never asking the birthday question in the first place, and it's clearly got Machino frazzled at the end, there.
So - if the purpose is to see Nitanda "grow" a bit and bloom into his full potential within high school of being more outgoing and, while retaining the core of himself as a dominoes/animal enthusiast who has his quiet little space, also expanding his world and himself to making friends and doing additional things outside his little club room - then having Nitanda be the one who ends up pursuing romance with Machino being the one who on the receiving end would fully complete that shift, and the flip of the dynamic between them to portray the extent of their balance against one another as a unit.
Not sure if that's the intent, or if it even needs to be, but I find the notion interesting.