Man I just made it up to the strike on venus and there was prolly 8 cutscenes totaling a half hour that got pretty in depth on what you're doing and why.
It ain't great but it's more than a mindless hoard mode and more fleshed out than, text at the beginning and maybe a cutscene at the end. During the missions there is a ton of exposition explaining stuff too.
The quality of the story is a little mediocre though. They jacking tropes from Mass Effect and shyt
But it's interesting enough, and the world itself is awesome.
I don't think it's fair to say there is barely a story though, especially only using the beta as reference, there is much more stuff going on after you leave Russia.