TL;DR - Yes you can - they are separate services and you can use them either independently or combine them if needed. You pay only for what you use.
Google Compute Engine
The first youtube video link you shared is for using Google Compute Engine (GCE), which is an IaaS (Infrastructure as a Service) option in Google Cloud. You can use this to set up VMs, custom networks, instance groups, load balancers and other infrastructure.
Google Cloud Vision
Google Cloud Vision is a more specific service which helps you with just Image analysis. It is a service independent of Google Compute Engine and you need not use Google Compute Engine to use the Cloud Vision APIs (although you can do that too if you wish in the future).
In other words - yes, you need not pay for Google Compute Engine to use just the Cloud Vision APIs.
Both Cloud Vision and Google Compute Engine are cloud services part of Google Cloud Platform. Both of them require first creating a project (using Google Cloud Console) and setting up billing before you can use either of those services (or in fact any of the Google Cloud services).
Trying the Cloud Vision API