TLDR: according to independent investigations by journalists, the object shown on the Al Jazeera video feed does NOT seem to have caused the explosion at the hospital.
What caused the explosion at the hospital is open to debate at the moment.
Al Jazeera Video
An independent investigation has been carried out by the New York Times:
The missile seen in the video is most likely not what caused the explosion at the hospital
CNN carried out an investigation as well, and the conclusion was:
CNN was able to determine that the projectile captured in the Al Jazeera broadcast was likely fired from inside Israel, not from Gaza, as was previously concluded, and unlikely to have any connection to the explosion at Al-Ahli, miles away.
The Washington Post investigation concludes:
Experts said that the widely circulated video probably showed an Iron Dome interceptor missile that collided with a rocket more than three miles from the hospital and most likely had nothing to do with the hospital explosion.
What caused the explosion?
New York Times:
The Times’s finding does not answer what actually did cause the Al-Ahli Arab Hospital blast, or who is responsible.
CNN:
The open-source imagery showed a huge explosion and destruction from the fire at the hospital complex, which experts said was consistent with a failed rocket crashing to the ground with unspent fuel.
Weapons and explosive experts with decades of experience assessing bomb damage, who reviewed the visual evidence, told CNN they believe this to be the most likely scenario – although they caution the absence of munition remnants or shrapnel from the scene made it difficult to be sure. All agreed that the available images of evidence of the damage at the site was not consistent with an Israeli airstrike.
The Washington Post:
None of the more than two dozen experts consulted by The Post was able to say with certainty what kind of weapon struck the hospital grounds or who fired it. But munitions experts agreed that the damage at the hospital was consistent with a rocket strike.