HTML Tidy seems like a powerful tool although I am having a hard time to find from their docs whether they do simple validation (I guess it does given that you ask the question).
This html5validator gives you a simple yes/no answer whether some files are HTML5 valid. It is based on the same backend that powers https://html5.validator.nu/.
It can be integrated in continuous integration. The README contains example configurations for TravisCI and CircleCI.
I think the continuous integration is key to emphasise.
HTML Tidy does validation as its default action (tidy <html file>), but unlike this, it doesn't seem to be able to target an entire directory (html5validator --root <directory of html files>), so there's another difference there.
It really brings special relativity home to think that the ESA's counter is only valid from the reference frames we usually use. It's only when Randall's counter reaches zero that we can unambiguously say that the probe landed in the past.
