[Video] An Israeli interceptor missile misfired and appears to hit a building in Tel Aviv

No. The one in OP's video was in post-ascent mode and not full burn and was spiraling wildly all the way in, but the one in the video you linked was clearly in terminal descent phase and flying far too fast and straight to be a match for OP's trajectory.

It did but interceptors do not create huge dust clouds. Here is a closeup video of another interceptor failure in 2023