why do his movies look so dated?

Agreed, and even that one's just a once watch affair for me. It's by no means a bad film, it just feels somewhat quaint and perfunctory when compared to something like Gone Girl, for instance. The original ending they filmed but later scrapped for the sake of commercial appeal, robs the film of any long lasting impact it could've had. As is, it's just a competent but somewhat routine and unremarkable marriage suspense thriller.

Overall, Lyne wasn't a terrible director but he certainly didn't amount to much other than being a MTV visual stylist. Like his contemporaries (Ridley Scott, Tony Scott, Alan Parker etc), Lyne was really only innovative for being one of the first major Hollywood directors to have come from an advertising background. Unfortunately for him, though, that also happens to be his weak suit, as none of his films ever felt particularly nuanced or thoughtful (or if they did, it wasn't because of the way they were directed) as Adrian was clearly more concerned with lights and cameras than story (but even then, as said before, the visuals in his films are largely dated).

I have a theory that for every director, the way their early works were made, dictates what their approach to filmmaking will be for the rest of the career, regardless of size or budget. David Fincher for instance, is another director largely defined by his early commercials and VFX work with ILM, as he remains very much the visual stylist and powerhouse technician he's always been. Difference with him, though, is that Fincher gradually grew and matured as a filmmaker, whereas Lyne really didn't.