First of all, the listing is misleading. The listing is political propaganda rather than reality.
The place is in Jerusalem, not in "East Jerusalem", and of course it is in Israel.
It is important to understand for people who are new to Jerusalem.
There is no such division. It is one city and one country. No borders to cross, no visas, no passports. You just take the light rail and get off at the Damascus Gate. And you are there.
The place is not under the "Palestinian Authority" government and both Jews and Arabs are freely walking around here.
Having said this, the place is not exactly clean, and the humus is very oily. So if you'd like to gain a little weight it is great.