I find it strange, weight lifting is already anaerobic. What does restraining the blood flow do? Limit lactic acid formation? Why would it improve strength gains? The break down of muscle tissue is what causes the rebuild and the gain to occur. Less sore means less break down.
It's not necessary to train at all to build muscle, as studies using exogenous testosterone have shown it to be extremely effective for muscle gain on it's own when raised above natural levels. Low testosterone men generally gain muscle mass as well when levels are raised. It hasn't been clearly demonstrated that men with levels that fall within the low normal range of testosterone gain muscle by raising their levels to the higher end of the clinically normal range. I'd love to see a study on that actually. That doesn't stop most "natural" lifters from taking a variety of things with varying degrees of scientific evidence. Personally, I take Boron and Zinc to increase testosterone and hopefully muscle mass but I don't take creatine. I try to never eat soy, or flax seed. I naturally have relatively high blood creatine levels without lifting and my doctors and I have decided against supplementation. Studies seem to show creatine works very well for some and not others. Your use may vary.
The claimed mechanism is that the method changes hormone levels that are conducive for muscle gains by tricking the body that is has worked hard and needs to adapt. There is some evidence in the medical literature where the body can be tricked. Ketogenic diets mimic fasting in many ways and some of the subsequent biochemistry changes. It looks like routine sauna use mimics exercise with some of the same biochemistry changes. I guess I'm saying this method might have some truth, but honesty I've never seen the research. Keep in mind, this constriction method is not commonly used in the body building industry and those guys will try anything. The fitness industry regularly makes incredible claims with little to no scientific support.