Learn English – the antonym for client-server

My first suggestion would be a client. I don't agree that it necessarily implies a network connection, but I can see that it could be interpreted this way.

For the operating system I think the association to a network connection is even weaker, so I would definitely call it a "client operating system" to distinguish it from a more server-oriented OS.

Alternatively you could call the computer a "desktop computer" and the OS a "desktop operating system".

I would use either of the terms you identified, deny or reject. Deny is a more neutral phrasing, with the definition to refuse to agree or accede to. By not approving their requests, you are refusing to agree to them, i.e. denying them.

Reject has a similar meaning, to refuse to grant, or, to refuse to accept. I would argue, however, that reject has a more negative connotation than deny. I might be upset if my request were denied but I would be angry if it were rejected. Rejection has more of a sense of repudiation than denial. I don't know if this is a universal connotation; I'm sure the comments will discuss that.