iOS Face ID validation invoked when browsing in Safari

Face ID should only ask for verification in Safari when using Autofill to fill in a username/password. I attempted to duplicate your issue myself with both Safari and Google Chrome, but received no such prompt for verification. Do you have an account on this website? If so, perhaps there is a login box somewhere on the website's home page that Autofill is attempting to fill. If not, it may be a bug with the website, Safari, or your OS. If it is a website bug, requesting the desktop version of the website and seeing if you are still promoted for Face ID could be a good test of that.
If all else fails and it annoys you too much, contact Apple.