Is there a way to access this engine without having to install the epic or coregames launcher? (and without having to build from source)
AFAIK there is none. You have to accept their terms, it is not open source.
If the source code is publicly available, it's Open Source, however much we may dislike the actual license.
It is not publicly available. If you click on this link you get a 404 page: https://github.com/EpicGames/UnrealEngine You actually have to go and subscribe, agree to their terms, and then you get to view the source code. It happens to be free, but it is by no means "public". (I also don't have a problem with their license. Their business model is more than fair.)