itch.io says I'm required to give my billing address before I can purchase the digital files. Is there any other way to buy this?
Not without sending cash through the post, no. Requiring a billing address is a pretty standard anti-fraud measure.
Everything else I've bought on itch was purchasable with just my card, no billing info required.
I guess you'll have to ask itch then, I don't have any control over how their site works.