No, the suit doesn't seem old and dated.
Yes, 2 buttons are hot right now, not 3 buttons. I'm looking at, instead, the gorge and it's fairly high wheareas 1990s 3 buttons jacket featured a much lower button stance; plus, the palcement of the notch in the lapels seems about right for current suits. Suits from the 90s featured a very low notch placement.
Also, 90s suits had very broad shoulders whereas the shoulders on this one don't seem to be football player wide.