Not anthropomorphic, because we'd easily recognize, say, an octopodal intelligence.

More like DNA-centered, perhaps?

Here's the thing - we have no idea if life, pick your definition there, is even possible outside DNA.

Hold your horses - I'm not saying it isn't possible, I'm saying we have absolutely no information at all.

For all we know, every photosphere of every star is teaming with life, and gas giants too, and some large portion of systems with a lot of free, accessible energy have life, wherever they are.

Or for all we know, we are literally the only intelligent beings in the universe.

I think both of these seem improbable. But I really have almost no basis to argue. We have two pieces of information: life definitely exists on Earth, and we have no evidence at all of life anywhere else. You really can't make any conclusions on such sparse input.