More questions than answers here. What the heck is going on with some of the bikes in this video and how am I just seeing it for the first time? Heretofore I thought of a pushbike as something your 2 YO straddled as you walked around the block.

Tasmania, represent.

Both definitions are correct.
Pushbike might be a good alternate name for a non-motorized bike, a non-e bike.

In plain English, I believe people can use whatever words they want, in theory — no correct or incorrect as long as the idea gets across.
But in specialized jargon like in the bike business, push bike can only mean a pedal bike, as opposed to a motorbike. It has had that definition for maybe a hundred years. More in British commonwealth countries I believe, less common in the US. Common in Australia I've heard, though I've never been there myself. Can anyone confirm or refute that?

I don't know if there's an accepted generic term for those toddler bikes. I've heard "balance bike" a lot, and it works for me, though I prefer Laufmaschine, Draisienne (French spelling) or Draisine, or the somewhat pejorative Dandy Horse. Those names refer to the adult version invented in 1817 by von Drais, but they're functionally the same as the modern toddler bikes. Shall we disinter or exhume the word Draisine for the tyke bikes? Nah, not catchy enough.

The Jargon Nazi has spoken!

"Push bike" was a generic name for a bicycle here in New Zealand for several decades last century, still comes up occasionally when bicycles are being listed for sale by older people.
A scan through these current bicycle for sale listings shows it's in more common use than I thought 🤔
https://www.trademe.co.nz/a/search?search_string=Push%20bike&page=2

Didn't listen, but I see wino bars, clown wheels, a penny farthing, some guy trolling (successfully) on a tandem and clueless riders blocking what appears to be a major thoroughfare. When I was touring Europe (fifty years ago this summer) "pushbike" is the term used by the English folks and an Australian lady I met along the way.

Fun song, but :53 looks alarming.

Word.

Here in 'Straya bicycles are often called push bikes to differentiate them from motor cycles, or motor bikes. We even have a bike shop called Pushys.

The bikes in the video that are bobbing up and down have their wheels laced with the hub off centre:



Which mine usually end up looking like unintentionally.