I'd say this is a very poorly phrased survey question, so it's natural to find it confusing.
It looks like it means to ask:
Do you have multiplayer features where a server (possibly but not necessarily cloud hosted) maintains the shared game state and sends updates to all players in that session?
Do you communicate with a server for other features, like login authentication, downloading news/updates/special event content, logging to leaderboards, maintaining an online inventory / saved progress, etc?
But I'd argue it's using the wrong wording if that's what it wants to know.
Authoritative is a description of the server's responsibilities. An authoritative server does not just relay client actions to their peers. It takes a role in vetting the client's report and applying only valid changes to the game state/simulation, and communicating that authoritative account to the other clients.
Cloud is a description of where the server is hosted. In contrast to a dedicated server running on a specific machine, a cloud-hosted server is a program uploaded to a service that maintains a fleet of machines, and can spin up one or many instances of your server program across that network on demand.
REST is a description of how communication with the server is structured. I won't repeat the whole definition here since it's covered comprehensively elsewhere.
All 8 possible combinations of these keywords can exist. I've built a cloud-hosted authoritative server that communicates via a REST API, for example. (For an asynchronous game, so peers could pull down the latest authoritative state with a GET request) So I'd say they're not the right terms to use for this question about users' server needs.