How do big sites rank for a keyword without that keyword in their backlinks?

So I have read all about on page, keyword density, I have between 1 and 2% keyword density etc, and I get to position 7 at the very most. I have a total of 2500 links built to my site, have a DA of approx 30 and PA of 41, but cannot climb any higher.

I also have backlinks with the keyword in at 10% and lsi at 40% etc.

2 sites which rank at pos 3 and 4, don't have the keyword on their page and don't have the keyword in their backlinks.

1 site has 20000 backlinks and the other has 4000….

How do big sites rank for a keyword without that keyword in their backlinks?