Your eyes are not deceiving you. The man pictured is NOT Woody Allen. It's Dennis Boutsikaris. Here, that's a more
recent picture.
Who is Boustikaris? He is one of those "Hey, it's THAT Guy!" character actors. On TV, you might have seen him on "Better Call Saul", or now on Apple's "Sugar". On the silver screen, he appeared in "The Bourne Legacy" (that's the one without Matt Damon, so you probably didn't see that), or that all-time classic, "Crocodile Dundee II".
Boutskiaris is Jewish, despite the Greek last name. He was born in the former Jewish hotbed of Newark and grew up in New Jersey as well, in the not-so-Jewish-hotbed of a town named Berkeley Heights. He's been active in Hollywood for a good 50 years, mostly in background roles. (Alas, even in "Crocodile Dundee II". He played Mick's girlfriend's sister's ex-husband. Aren't you glad you asked?)
So what's with the getup? This is from one of Boutsikaris' starring roles... in the 1995 miniseries, "Love and Betrayal: The Mia Farrow Story".
Perhaps we should have stuck with the more recent one.