The Toshiba Sampler is the only version of The Next Tetris that exists. Years ago I mocked up NUON DVD box art for the game (so I could put it on my shelf along with the rest of my collection) and put that up on NUON-Dome for anyone else who may want to print it out and do the same thing with...
Your best bet now is to grab the freely-downloadable NUON Homebrew DVD that @EdgeConnector made. It has a bunch of the stuff that was on the Games+Demos disc: https://www.nuon-dome.com/download.html
haha yep this is almost all content pulled from N-D and the video embeds are from my YouTube channel. All those videos were in old, outdated formats and I figured they'd get more attention on YouTube. Mission accomplished!
Tetris didn't come with a manual, it was a disc-only release.
Archive.org has manual scans, FreeFall included: https://archive.org/details/manuals_nuon