Why not ask? If a guy asks a girl (or vice versa) to go somewhere and it's not abundantly clear it's not a date (e.g. you've done similar things together before, they're openly gay, or they explicitly said it's not a date), then it should be assumed to be a date unless clarified otherwise. So if they don't specify and you're unsure, then ask.
That said, her leaving is also odd. A misunderstanding shouldn't be a big deal. Show up the next day and laugh about it, and you're golden. I wouldn't be mad if that happened to me, nor should either anon or the girl. It's just a misunderstanding, it's really no big deal.
That's just how social expectations are. I recommend you go ask a handful of single men you know (i.e. coworkers) whether they'd consider a 1:1 outing with a woman to be a "date." I'm guessing most would say yes.
Exactly, they're coworkers where OP isn't certain if they were flirting or just being friendly, and other coworkers confirm she's flirting. To me that means:
they don't have a good enough relationship to tell the difference, so probably not "friends"
other coworkers don't seem to experience the same thing
claims to not have other friends (surely she'd mention a BF, no?)
So to me, that sounds very much like she's flirting, so it's totally understandable for OP to consider it a date.