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The site is related to the key terms however these are specific competitor multiple brands key terms which seems to rank very well for considering the brands aren't mentioned on the website.

I've checked backlinks, anchor texts, internal site search etc and nothing coming up for the brand terms and yet rank well. Trying to figure out how this is possible...

As far as I know, it's not normally possible for a website to rank for a keyword that is not mentioned on the website. I have seen a website that ranks very well for key terms and yet they are not mentioned anywhere on the website, I have run advanced search & checked using tools including cloak checker on my findings.

How can this be?