People seem to think that Chucks are magic or something. The reason you see them recommended so frequently by lifters is that they used to be the only widely available brand of sneaker (for men, at least) that didn't have a puffy, cushiony sole. As I keep saying, this is no longer true. Thanks to the mainstreaming of skateboarding, "barefooting", etc., there are plenty of shoes, like yours in that clip, which offer the same exact benefits that Chucks offer.
So, instead, save up to get a pair of real lifting shoes. Real lifting shoes have a slight heel (a wedge sole that is higher in the heel that at the toe*); a wide, hard, non-compressible sole made out of something like wood, very hard rubber, high-tec composite/plastic of some kind, etc. and which does not allow for any kind of rolling of the foot in any direction; and construction that usually includes a metatarsal strap to help suck your foot firmly into the shoe.
In other words, a lifting shoe is a shoe designed for lifting. Chucks are just one of the least bad mass-manufactured sneakers.
* An exception is a certain brand of PL squat shoe, which has a negligible sole gradient, but has a stiff, high-top design that is more for lifters who keep very vertical shins, so not good for SS:BBT-style squatting. Plus that brand is pretty expensive.