@givemersspls
If Keisuke knew that Kaede had romantic intentions, then it would make more sense because then Kaede would arguably be trying to monopolize Maiko
If Keisuke is aware of Kaede's intentions, I think he would have let them have their date out of consideration for his big brother and Maiko. This kid gave up football because Maiko made a passing comment about baseball being cool. And with this particular hypothetical case,
Keisuke would be more aware of Kaede's romantic feelings towards Maiko than Keisuke's own.
While Keisuke does act childish, he isn't that sort of 1-dimensional character. Not every character has to follow the same pattern. Does that make sense?
What Keisuke sees is two friends spending time together. Keisuke is like no, fuck that, you don't get to spend time with friends unless I'm okay with it.
He was just tailing them for a while until Kaede left Maiko alone to be bothered by some strangers.
The "she is mine!" statement came from the flashback with Kaede spitefully saying, "don't go thinking Maiko is something can keep for yourself", and after Kaede trying to coax out a reason from Keisuke for why he was following them. Before all that, Keisuke seemed content with just following them to the point of denying that he was even following them.
"Now, in both time and reality, Maiko, have you chosen to be my woman?" is just Keisuke playing along with Kaede who suggested a contest with Maiko as the prize - it wasn't some serious psychotic shit.
Now that I think about it, maybe Kaede the schemer is being considerate for his little brother too? Perhaps being told that you love someone is a little sleazy? It's obvious that Maiko is head over heels for Keisuke, and Keisuke cares for Maiko, but Keisuke is ignorant of romance. Maybe Kaede is taking advantage of the situation and his own romantic feelings to provoke Keisuke?