You could use the Parallax Scroll plugin. Instead of the way of that video you mentioned, the Parallax effect is obtained by putting a shortcode on a page. The result is the same, but in the settings, you can let the used picture scaled down for mobile, so that at least that picture itself is shown at mobile phones. It is not what I want, but it helps a bit.
The plugin was updated 11 months ago, but this morning I got an email from the maker of it, saying:
“The plugin should continue to work with new WordPress versions, unless WordPress were to fundamentally change how it works.”
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This reply was modified 7 years, 2 months ago by gunivortus01.