In centuries past, and even till the mid 20th century, it was common to hold the bowl-back instruments without a neckstrap and playing while standing. I am less familiar with ouds and bouzoukis in this respect; I have more experience with lutes, mandolins and charangos. But I think of the bouzouki as a mandolin-family instrument, and expect that the same is true for it.
To do this, you have to have your right arm run approximately across the tailpiece - and notice that many of the tailpieces are designed to double as an arm rest - the instrument has to be held rather high, across your chest, and you have to not be dependent on being able to watch your fingers as you play. It's really not as difficult as it looks like it would be. The hand position that initially caught Bass's eye is typical for this style of holding the instrument, except that the arm position and the position of the instrument are in the modern lap-sitting position.