I'm developing an application that has no client-server connection by design, all of the work is done locally (no internet connection needed), so I'm wondering if I can call it a client? (I'm asking for documentation purposes)
You can only call it a client if there is some sort of server it communicates with.
Whether that server exists within the same process or is on Mars is irrelevant to the terminology. Also irrelevant is the incarnation of the server. It could be a separate machine but also an object with an interface in the same program.
The point is that the server does something for the client. You are not a customer until you talk to a shop owner or other kind of vendor about acquiring some service or some goods. You can only be a partner if there is someone else.