Actually, I take back what I said about it probably being cellular. It's possible they're cellular, but I don't know where I was looking before – it said the price for a non-cellular iPad mini was $299, and cellular $399, or something like that – but I don't think that's accurate. iPad mini with cellular is more than $400, plus the monthly data.
It would probably make more sense for them to be Wi-Fi iPad minis, tethered to a phone with cellular data.
Showing videos is, I'm sure, one of the reasons why a bigger screen is required. Not to mention – could you imagine using such a small screen for a full-featured area book?
Also, the most recent versions of iOS have pretty good theft-deterrent systems (not perfect, but much better than before).