Alice is a strange story. Maybe the fact that it is episodic and doesn't necessarily have a point that it's working towards makes it scarier? Like, the rules all seem rather random. Another book that isn't random but that I found kind of scary was Catherine Fisher's Incarceron--because well, firstly the world is kind of a grim one, and secondly because I felt whenever I understood the rules, I'd find out something new, and have to shift my understanding of the rules to something bigger (and scarier).
And yes--you're right, Arty. When you follow the MC through the portal, it does feel intimate. You leave the rest of the world behind to take that journey with the character. It feels more real and more vivid. (I confess that I um...do indeed have a painting of the Dawn Treader with water spilling out of the frame on my kitchen wall. Because portals.)
A portal story I really like is the webcomic The Dreamer. It's time travel and makes you have a ton of questions about both the past (it's about a modern teen going back to 1776 in Boston) and eventually, about how both of the worlds even connect, and what the rules are between them. Or W--Two Worlds, which is a TV series about a webcomic, and people traveling back and forth between the comic and the real world. I'm finding the same questions arising--what makes all this possible? It's the guessing and trying to figure it all out, mixed up with the tension of characters trying to find happiness across an impossible barrier, that I find intriguing.
There are real life portal stories, too. In a way, every time I've moved has felt a little bit like going through a portal. I can cross back and forth--but the two worlds never entirely, completely, line up. Maybe that's why such stories appeal to me so much.