Strict mode is quite different in TypeScript than JavaScript. You enable it in tsconfig.json (not per source file), and it's now enabled by default in the template files created for you by the Firebase CLI when you create a new TS project. Enabling it actually requires you to do a fair amount of extra coding to get the types right in some circumstances. Some people might not find that necessary or helpful for smaller projects. For larger projects, it's crucial, but that's rarely going to be the topic of a 5-10 minute video.
I can only imagine that "use strict" is not included in video resources that use plain JavaScript, because it's not required to learn Firebase. Most Firebase videos don't attempt to teach programming best practices so much as they attempt to teach use of Firebase products. It's up to the viewer to determine their own best practices.
Doug