The people who were kids when the movie came out are in their 40s now. It was special in a way the re-re-re-makes of recent years haven't been. So I can see some adults enjoying it on their own, beyond sharing it with their kids.
Something like Frozen, yeah it's for kids. It's too new for its audience to have grown up. Aladdin, though, was still at the beginning (middle?) of the new golden age of Disney animation, with a good dose of the sensibility that makes real golden-age animation last: it knew how to aim at both adults and kids without tipping wholly in either direction. There's enough to keep adults interested that goes over the heads of kids without diminishing what they see.
Does that translate to enough childless adults to sustain the Broadway show now? No, probably not. But it's not exactly a "kid show" in the way that some are.