Aldi do not have an ATOL to sell air holidays by the looks of it.
So they are either
1. Selling components (split-packaging), not covered by ATOL (like Travel Republic and OTB).
2. Or maybe selling as an non-ATOL agent, holiday packages from an ATOL Tour Operator. Which I doubt.
Who knows? Of it's not clear, ask yourself why? Just because ALDI are a big chain store doesn't mean a thing in my books. After all, Woolworths has been around for much longer and what has happened to them was a surprise!