I would expect that the setup described would be best for smaller pieces of log, and as is indicated the main use is for splitting half-splits to small "loglets" for a decorative burner.
One of the 3-way or 4-way wedges already linked would likely offer easier "stable mounting" of the wedge, and as described at one link a few old tires would make a usable "cage," or - as the original tool is described - a simple back-board to lean the log on would likely suffice.
For a reasonably compact manual splitter for smaller logs, something like the AGMA Smart-Splitter might be worth consideration when the existing setup wears out. The "slide-hammer" construction gives significantly better control for most people who haven't grown up driving rail spikes for train track, and is considerably easier on the whole body if one is not in shape for swinging a maul.
I would be concerned somewhat about the picture at this link, since forceably driving bare knuckles past the exposed end of the guide pipe makes me cringe a bit. Broken knuckles are not a friend of the musician. I believe I would look at putting at least a rubber crutch tip or bicycle handlebar grip on the end of the support pipe, and would likely wear a pair of White Mules for the splinters.
Slide hammers for driving fence posts (chainlink fence) are available in a small (6 pound, I think: mine was about $25 US) for run-posts, and large (I believe mine is a 12 pound: $35 US) for end and corner posts, and are very much safer and less strain on the body than sledgehammers. The post hammers also have "handles" that make the lifting easier. With a splitting wedge mounted below, and a short section of fence post (guided loosely) above an improvised setup should be quite simple to build, and quite economical for occasional use. A splitting wedge mounted on the end of a short section of post could also be used in the conventional way, one would expect.
Nothing quite like the description appears in the first hundred pages of my Google image results, since - for good reason - most people who buy a splitter are interested in hydraulic or electric powered ones. Since big boys with their big toys invariably buy "more tool than needed," the used market might offer reasonably economical power splitters for one who can justify one and pokes about a bit, although in areas where there's a lot of wood to be split there may be few willing to give one up. Try the Chicago want adds, maybe(?).