If you don’t physically own the hardware on your books as a capital asset and depreciate it, regardless of where it is deployed it is “in the cloud”.

If you ship a server to a data center and maintain it 100% yourself paying only for power, data, and an occasional hands on switch flip, it’s not cloud based, it’s a compute asset.

Here is the easy way you can tell. If your contract with your provider has an SLA provision that specifies physical hardware up time, it is cloud based.

NIST 800-145 clearly classifies VPS as IaaS which means it is considered cloud computing. If you wanted to make this argument a better standard to quote would be ITIL for cloud services or perhaps ISO/IEC 27018 or FedRamp as these actually have different standards and callouts for VPS. Besides these however all other standards are pretty agreed that a VPS is considered cloud computing.