I could not say what constitutes a legal die re-roll, let alone what defines it to become legal but from the video you have posted, I must say that this is a practiced die roll.
The d10 dice we have look like an upright diamond with an upper and a lower half. One of the halves has the odd numbers while the other holds the even numbers and it was apparent in the video that the die is being placed between the palms with the side of even numbers being on top and it's spun from that position. And if it's actually just a die you're re-rolling and with practice, that method significantly increases your chances of scoring a crit from just 10% from the re-roll to 20% since the odd numbers won''t come face up. It also decreases the chances of scoring a gray from 30% to just 20% since the side that has 1 and 3 won't come up.
As a judge, I would consider this as a practiced roll and it categorically falls under cheating.