All this was already hinted at throughout the Batman Beyond series anyway.
It seems a bit weird but I don’t mind it all that much I guess. Maybe because I’m a huge Babs fan.
That was the one part of the DC Animated Timm-verse that I never truly bought actually. From a recent interview at Comic Con, it seems that Bruce Timm really does think the relationship is inherently romantic, citing how it was played off in the Adam West show. But, I never really read Batgirl that way.
To me, Batgirl always seemed part of the second generation of Gotham crimefighters, which makes her and Robin the obvious (and much more tasteful) pairing. Batman, as the original Gotham crimefighter, should be the only first generation father figure, raising the so-called “Bat Family” to succeed him. Even in the last season of Batman: TAS, Timm tried to make Batgirl into a “mother” figure.
I far prefer the notion of either a Batman-Wonder Woman or a Batman-Catwoman relationship. The latter particularly is interesting because of how Catwoman is probably less crazy than Batman is. She could potentially help his mental health, while he helps reform her criminal behavior.
Then, of course, there is the gender politics, which is less of an issue to me personally, but one with which I can sympathize. The original comic was already derided in some circles for its callousness towards harming Batgirl, but the adaptation (shockingly) seems to worsen the situation, essentially reductively defining Batgirl as a woman, to be sexually desired not only by Batman and the randomly added gangster fellow in the first 20 minutes but also the Joker.
First off, there was no sex scene. Batman and Batgirl kiss and you could infer they had sex, but we don’t see that.
Batgirl actually explicitly states to Batman over the phone: “It was just sex, for god’s sake!” So, no inference required for better or worse.