So the option you have is using stale data dumps. They're reasonably workable, I even host low-markup versions of every wikipedia article myself in my home lab and it's like some 100 Gb worth of compressed data, images excluded. Uncompressed I don't know where it ends up, but below 1 Tb at any rate. Manageable but very unwieldy. File systems like ext4 struggle with that number of files in a directory so you need to be a bit crafty, but it's not hard to get around. If all you want is an info box, you could probably squeeze it down to a couple of hundred gigabytes uncompressed. Definitely not something you need a data center for.
The catch, as mentioned, is is that the data is a stale snapshot. The only way you are getting current data is on the main site, which may be a problem if you have ambitions of staying up to date. I personally don't mind. I figure they used to sell printed encyclopedias and that worked pretty well so having a 1 year old copy of Wikipedia isn't that bad.
It's also a sort of weird domain. I can see how it might not be easy to host in the cloud in a way that's both affordable and performant. Since so many insist on cloud-based apps nowadays, there's probably a market for Wikipedia APIs with a good SLA.