It's genuine... but not exactly desirable - a lot of these 1960's ladies cocktail watches are surfacing at the moment, and they wear tiny (even on a lady with a small wrist). If you're not a lady who wears a lot of formal wear, this isn't really all that useful.
I know nothing about watches, can you ELI5 (about the lack of chronometer, what exactly that means and why it's so desirable)?
I could. Or you could google Omega calibre 671 and find out for yourself. For future purchases, it's recommended that you do research BEFORE, you buy.