I just can't quite figure this out. She's dating him. Doesn't that make him her boyfriend?
Not necessarily. "Boyfriend" means different things (and different levels of commitment) to different people. If you go out on a date or two with somebody, that doesn't necessarily make them your boyfriend. It can, if that's what it means to you, but it doesn't necssarily.
And why would you date more than one person (this would be referring to her use of the word "exclusive"?
Because you're not serious about any of them yet and vice versa?
Because you have an open relationship with all of them?
Am I just naive for thinking that being exclusive should be a given in any relationship like that?
Yes, and kind of ignorant. For one thing, plenty of people are capable of open or polyamorous relationships. For another, "light dating" can be with several people, because it's not gotten serious yet, even if you ARE monogamous. Please, be careful saying things about "ANY" relationship.
Am I naive for thinking that dating = boyfriend/girlfriend?
Not naive for this, really. But "boyfriend" typically implies a deeper level of commitment than "dating"'s early stages. Dating can include Boyfriend, but doesn't necessarily. Furthermore, these terms are highly subjective.
Wouldn't not being exclusive be like cheating on your partners? Whether or not they knew, that's how I would feel.
Cheating is nonconsentual. If they're fine with it, it's not cheating, and it's not harmful or wrong. If you couldn't handle that kind of relationship, fine--but some can.
And not being exclusive after a few dates just means you aren't very committed, to me. Because, come on, a few dates hardly equals a serious monoamorous relationship.
I just don't understand
I am not yet born, console me.
I fear that the human race may with tall walls wall me,
with strong drugs dope me, with wise lies lure me,
on black racks rack me, in blood-baths roll me.