In my opinion, the request is a bit ambiguous, and you need to ask for clarification. We are not talking about the data, which of course should be private, that's obvious. The question seems about the server: what is a "non-public" server? What we call non-public is probably going to be something private, I guess.
A private server is generally a server that you don't share with other people. This could be a virtual private server, where your server is actually a virtual machine that runs on a shared physical machine. Or it could be a physical private server, also known as dedicated private server, which is a physical machine that you don't share with any other users. Your dedicated server could then be in a colocation data center, or it could be in your own facilities.
There's also the distinction between public networks and private networks to consider: if by "non-public server" they meant "non-publicly-accessible server", then that would be a server placed in a private network, only accessible from the company's network.
Google Drive probably doesn't fall into any of the above definitions, because the use of their servers is shared between several users, and the servers are accessible by anybody on the internet. As I said though, if you want to be sure you would need to ask for clarifications on that part of the policy.