"placed behind the taxpayer access wall using their embed video software Wistia.

This is new this year, and the Wistia software doesn't allow one to copy the URL to share the video or view it directly on the hosted site."

Okay. This was your Title question:

"Can you provide the URL link to the demo video that is provided to taxpayers when they sign into Intuit Link for the first time?"

And you just answered that with: No.

I played some of those videos and while they are playing, you can right click them. There are three options given:

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Copy link and thumbnail <== This is what you wanted, right?