The "blood marker" in question is anti-COVID antibody titer. That's not genetic. (It may turn out to have a genetic component, but that has nothing to do with this article.)

Was there ever a doubt about this? After all, if you don’t have a fairly standard human immune system the vaccine isn’t going to do anything at all for you.

So I know this isn't your point, but your comment made me think, does it actually require any type of human immune system? The vaccine exposes you to viral protein which causes an immune response. Wouldn't that work in other species no matter the implementation details of how their immune system generates that response?

and mostly probably life style

Probably, but the article isn't about genetics.