According to this paper, "The gauge integral [a.k.a. Henstock-Kurzweil integral] provides the only formal framework that is close to the original development of the Feynman path integral", and also "if one requires that a mathematical formalisation remains close to the original treatment in physics, then there seems to be no choice other than the gauge integral for the formalisation of Feynman’s path integral."

Is there any merit to these claims? I've been under the impression that there are a lot of ways to make path integrals rigorous in various settings, maybe some more successful than others, but I haven't heard of this one before.