The product promoted in the original post simply dissolves hair, like many over-the-counter hair removal treatments, and does not affect the hair follicle. An active follicle will continue to be active, and the hair 'bulb' will eventually extend the hair past the surface of the skin again. The fine print does mention that this works by dissolving the hair.
Vaniqa or Eflornithine will slow hair growth after several weeks of twice-daily application. It eventually penetrates the skin and mucks with the chemistry in the hair follicle to slow it down. The effect isn't permanent, and the active follicles will return to full-speed hair production several weeks after stopping it.