UPDATE: In the comments, Ali provides the translation:
The video starts with the soldier muttering faux-Hebrew gibberish. Then the lady shows up and the soldier says "hey you, where are you going?" in broken Arabic. The lady then says "where do you think I'm going? I'm going to pray at the holy Dome of the Rock Mosque. Is there a problem 'boss'?" The soldier then says a very long sentence in gibberish and the lady asks what that means. So he says "it means 'not allowed'. Go home, it'll be better for you and for me." So the lady turns around and says an Islamic phrase that means "there is no power or way without God. Listen boy, aren't you a Jew?" So he says "yes I'm a Jew. A proud Jew." (The word for proud in that context also means "cough", so he starts coughing). The la dy then says "So why are you at the Dome of the Rock?" So the soldier dismissively says "what do you mean?" So the lady says "I'm telling you, go home, it'll be better for you and me." So the soldier says "boy, go home or I'll shoot you in the head." So the lady says "boy, how dare you lay hands on a woman, you coward, you son of a Jewess? Oh look, a rocket from Gaza!" So the soldier cowers in fear asking "where!?", so she proceeds to beat him up and then says "it's ok, lying to the enemy is halal (Islamically ok)." The video ends with the two Jews on the ground saying the Islamic saying that you say when you're done reading from the Quran "God is right".
In real life, of course, Muslims worship there by the thousands and Jews are the ones usually expelled if they even move their lips.
However, there are rare exceptions. Just found this video apparently taken very recently:
I'm very surprised the guards let him pray. Maybe there is hope after all.
