Walking exhausts me. Walking with weight on my arms exhausts me in addition to hurting my back. Being able to sit upright and push myself along with my foot, letting the momentum of the wheels carry me further than the same exertion would with walking feels, to me, a lot easier than walking, using a walker, or trying to push myself in a wheelchair.
A couple years ago and for several year prior, this would have been out of the question for me due to the balance issues and also inability to exert myself that much. But at my current stage I'm capable of riding a bike, only problem...it exhausts me!
There's a couple issues to consider. One is that while bicycling requires less energy expenditure to get from point A to point B, compared to walking, it's generally a more intensive expenditure. It's difficult to guess how intense a non-pedaling bike would be, but that intensity still might be a problem for ME patients, especially if you add the struggle of posture and balance to the mix.
Additionally, you would be using different muscles than you usually do (arms as well - a lot of tension required holding onto handlebars), which might cause unexpected problems. Basically when we run out of energy, certain muscles are prioritized to get the remaining energy. Hence we can still walk a bit even when in pretty bad shape, but the muscles used to make this a more graceful process tend to cut out and we lurch all over the place. The muscles used in pushing the bicycle might not be ones that work when exhausted.
I think the general concept is interesting, but it really should be in a narrow tricycle design to minimize balance issues and to allow true rest. Yes, you can balance better on the bicycle shown above than on a normal bicycle, due to a much lower center of balance, but you still have to use leg muscles to hold that position. And it actually looks like a more awkward position to hold compared to standing up straddling a bike.
I think it would help with some issues (mostly leg and foot based, especially if one-sided), but have serious doubts about how helpful it would be for an ME patient who is having problems with insufficient cellular energy. For $300, I'd absolutely insist on being able to take one for a test drive. I can't say I care for such a brief return period - a 7 day window is a bit intensive when you might be crashed, etc.
This guy also leaves comments on various mobility articles using different girly names but pretty much identical text. Some comments appear to have been deleted (as spam?) since they show up on google but not on the linked article or its comments. And there's a complete lack of real reviews anywhere on the internet.
There are stores I cannot enter by myself because they're too big and I need places to sit down. I can go in with someone else pushing my wheelchair, but I'd like to be capable alone and an electric wheelchair would be overkill.
I don't think an electric mobility scooter is overkill, if you can't handle outings when walking. Definitely more expensive though, which is a major factor to take into consideration.
My reaction time isn't quick enough. 
