"I invited them to this event."
Translation:Zaprosiłam ich na to wydarzenie.
It doesn't fit the sentence, in my opinion. "zdarzenie" is just something that happened. So can be "wydarzenie", sometimes - although I'd go with 'zdarzenie'.. But "wydarzenie" can also be "an event" to which you can invite someone, something that is planned. "zdarzenie" doesn't have this meaning.
That example makes sense! I have been wondering if facebook is how "wydarzenie" became popularised in referring to social events.
But yes, when I think of telling someone in Polish that I'm inviting them to an event I'm hosting, I'd just be specific: "na imprezę", "na piknik". Just saying "zapraszam na wydarzenie" without providing any context sounds peculiar. (But in English it doesn't. One can say "I'm having an event on Friday, you should come", and people intuit that it's some sort of party.)