Egyptian soldiers entering Gaza to lift the siege and deter IDF raids is a demand common even among secular Egyptians. Probable and popular is a pact with other Muslim governments run by democratic Islamists; Turkey, Libya, Tunisia, and Syria post-Assad.
It's clear that Ikhwan is competing with Noor for the conservative and Islamic vote, which is the majority, so they make promises the Salafis can't top. There's speculation that these candidates are saber-rattling at Israel just to win votes, but as the Israelis say, if the new Egyptian government can't deliver on domestic promises they'll surely follow through with foreign policy promises.
MEMRI TV, btw, is run by a bunch of Israelis and American Likudniks. They translate any anti-American, anti-Israeli video they can find out of the Muslim world.