I've seen similar language recently (and have booked one or two). I agree it's prepay at booking, and you can cancel for a full refund up to 1 day prior to arrival. I also agree it seems weird to mix "nonrefundable and prepay in full" with an otherwise very flexible 1 day cancel. When I've seen this type of language for a rate, it's basically been properties dumping inventory they don't think they're going to sell.
Bottom line, yes, it's weird, but would you rather they combine "nonrefundable and prepay in full" with a 14 or 30 day cancel? I'll take this one, thank you very much.