Some link shortening services allow you to either bring your own domain or register a domain through them to use, so in the latter case it would be "via" the link shortener.

It's sometimes available on other types of SaaS services where your URL would otherwise be customer-facing as well.

Presumably they meant "by a" not "via a" . I wonder why misuse of latin words in English seems so common; see e.g. frequent confusion between e.g. and i.e. .

I think the author used the word correctly but explained the circumstances somewhat confusingly.

IIUC an entity engaged a service to register a domain on its behalf. So the entity did indeed register via the service, but it would also be correct to state that registration was carried out by the service. That service also happens to provide a link shortener. So instead of referring to the service as "company X" the author went with "link shortener".

I'd hazard to guess most people treat these things as just regular English words or phrases which have diverged in meaning, not even realizing it is/was Latin with a specific meaning. Particularly e.g./i.e., I remember them by the English translations and couldn't even tell you what the Latin they stand for is without looking it up.

Just go to the domain and find out.