so wait did he know her birthday or just prepare that video for whenever her birthday may occur
Didn't know her birthday; he'd prepared that video back in May when they had a break from school, and it's currently "late in June" with Machino's birthday being the week prior to this chapter.
Which I believe is meant as a counter to her earlier comment about how Nitanda "never reaches out" to Machino and how she's always taking the initiative in their interactions (and larger friendship). It's clearly true, and he feels bad about it, but he has his own little ways of being proactive instead of reactive, like this pre-made "for whenever" birthday message to her.
It's even done using Dominoes, keeping to his theme and thus a little bit of himself, is something that could be made in-advance for whenever the occasion actually arose.
And I think that degree of thoughtfulness on his part is what hits Machino so hard in this chapter: he
really does think about her even outside of their interactions in the club room, and he's not 100% just reacting to her presence each time.
That realization is what's got even her ears blushing in the last panel, I bet. If she wasn't already, she might be falling for him a bit now, too.