I’ve had Shapr3d for about 3 years, but barely used it, which is a pity. I’m now changing that. 
I have the same experience as the OP, about how the rotation works. However, for me it’s not always the same. Sometimes it works perfectly as I’d want it, and at other times in the same design and same session seen from the same angle, the rotation is totally different.
If I view the object from the right side, oriented by using the cube, vertical one finger swipe will rotate the object around a horizontal axis perpendicular to my view (parallel to the screen surface), just as I’d logically expect it to. This happens no matter where on the screen I put my finger. Great.
If I swipe horizontally, I would want the equivalent to happen. That the object would rotate around a vertical axis perpendicular to my view (parallel to the screen surface). Sometimes it does exactly that. Great!
However, most of the time it doesn’t. A horizontal swipe will only rotate the object around a horizontal axis parallel to my view, (perpendicular to the screen surface). This rotation is almost useless, as it’s unpredictable and mostly gives a very large rotation, depending on where I put my finger.
I’m at loss about why the same input works in different ways. I suspect there is something I do to cause it, but it changes during a single session on the same design. I use the exact same viewing position and get a totally different behaviour. Strange.
Another related issue that has no practical influence, but still might be a useful point, is the names of the sides of the orientation cube. If I tap the “Right” side, a bit of rotation will reveal that the “Top” is as one would logically expect up and the “Bottom” just as logically down.
If we name all sides of the designed object as they are related to us looking at the screen, the “Front” and “Back” sides are correct. However, this is perhaps not the best principle. A design object is worked on from all orientations. Most of the time the “right” and “left” we experience in our chair by the screen are not the one we see on the screen.
A much more logical and in my opinion more functional denomination system would be to use the same principles as on boats and similar. Boats, cars and many other objects have specific logical sides. Designing one in Shapr you will have to accept a reversal in either left/right or front/back.
Looking at the right side of a car standing normally on the road, the front is to your right and the back is to your left. If you start designing the car from its right side, the orientation cube will claim that its front is to the left, where the trunk should be. As mentioned, I know why this happens, and of course it also really doesn’t matter, but I think changing it, or making it a settable option, would be a (tiny) improvement.
The unstable horizontal rotation, however, is an important nuisance for me. Sooner or later, I guess I’ll find out that the reason is something I do, but whatever it is, it’s not intuitive, which is at least one topic to address.