Funny this post would appear this week. I was also in the area recently and found myself intrigued by the "Jerusalem Style" description on the sign there. Intrigued enough to pick up a menu. I will note that the daily special was not on the menu but written in Arabic on a chalkboard. Also, the bakery in the same strip mall, Prince, was exceedingly good.
Getting back to Jerusalem style, I highly doubt there is a connection, but surely "Jerusalem" food got a lot of publicity last fall with the publication of Yotam Ottolenghi and Sami Tamimi's book of the same name--as an aside, as much as I thought I'd love that book, I found I like Salma Hage's Lebanese Kitchen much better. Ottolenghi does include a recipe for the one item (that I know of) with Jerusalem in its name, Jerusalem grill, which in Jerusalem is a mix-up of various chicken parts with a good dose of spices.
More, on this forum a bit back, there was a disscussion of the differences between Israeli restaurants and "Middle Eastern" places. In my experiences, Isreali restaurants provide an experience, not better or worse, but different than other Middle Eastern restaurants. Yet that array of salads, including one with canned corn, remind me much of Israeli restaurants (really). So, maybe there is something more to Jerusalem style than religious/ethnic differences.
And it's always worth pointing out what a treasure this part of Chicagoland is for chow. While Dearborn has a few places more grand in design or offerings, I know of no New Yaseem Bakery yet around here, I really think the greater Bridgeview area can match pretty well.
Think Yiddish, Dress British - Advice of Evil Ronnie to me.