No. Ben Shapiro was not ever a child.
The song doesn't seem all that technically demanding but it does have a few tricky passages that Shapiro handles deftly. Seems to me. Actually, I couldn't listen to the whole thing. Not my cup of tea, but watching did remind me of a conversation I had with my dad.
My older brother and I found three old violins in our grandparents basement and naturally tried to play them. Impossible. There aren't any frets, we hadn't a clue where to start to tune one. None of the three were any good. We just made incoherent screeches and a mess of the torn up bows. My dad told me he hated violin lessons, his strong preference at the time was guitar like the cool guys played, but his own parents insisted he compete his violin lessons instead and that mismatch put him off pursing music altogether. He was no obedient Ben Shapiro at twelve. I said, "Violins don't even have frets! How in the world do you even know where to put your fingers on the neck?"
Here my dad switched to violin defense mode. His eyes widened then focused sharply. "Look, without frets you can get half-notes, quarter-notes, and even 16th-notes." Which makes a guitar very rudimentary and clumsy by comparison. And I appreciate that insight but recalling the basement discoveries I was still cold on fretless violins that offer no assistance with note finding. The whole thing still baffles me.
Comments on YouTube are amusing. Hardly any address the song or Shapiro's skill except to note that they too play violin and notice mistakes, and they remark on periphery Ben Shaprio and later day Ben Shapiro instead. But none of them remarked about how Shapiro does sound a bit like like Porky Pig when he gets excited which turns out to be rather a lot.
I found the clip interesting because it shows a side of young Ben Shapiro that I did not know.