So what is a lute and what is a ukulele? I would answer the question with this question.
There is no doubt that there is some marketing in the choice of product name, taking advantage of the current popularity of ukuleles. But there is more to it.
The bowl back uses an entirely different production process to the figure 8 shape. Looking at the pictures, the instrument has metal frets where usually the lutes have gut or nylon frets. The tuning is also different. Find some videos of lute making and uke making and see the differences. I think you might find that the bowl back shape can make the instrument much louder and more able to accompany instruments like guitars.
For an exercise look up the popular lute tunings, there are one or two which are very easy to set up on your GCEA or DGBE ukulele. One of them only requires a half step change to one string.
A major difference between lute and ukulele is the players. Lute players are happy to pay for a good instrument, they will even lease a student instrument to take classes. How many ukulele players would do that? The lute players also take to learning about music and how to play the instrument a lot more seriously and even learn stuff like reading music and Lute TAB. Of course some of these things are much easier if you have 400 years or more of history to help you out. Ukulele players are lot less tied up in history and protocol and sticking to traditions. Both approaches have their advantages.
Using another instrument, which is the right mandolin, the one used by Bill Monroe, or the bowl back one used by Italians?
What I like about the instrument in the photos is that it is about 21 Century musical instrument fusion. Whoever made it and came with the product name and concept is not happy sitting around playing 400 year old music, they are trying to innovate and fuse instruments to create something new. In the mid-20th century electric instruments were fine tuned and we had an explosion of popular music. Not much has happened since, the instruments are still based around designs from the 1960s. Maybe a lute - ukulele fusion can lead to something completely new for the 21st Century?
Since you have read this much waffle, why not take another 30 minutes to find some lute music and see if you can tune your uke to have a go at playing it?