It wasn't strictly HM, as it had extensions for the subtyping that lifetimes require. It was based on HM, however.
The new bespoke scheme gives approximately the same results as HM but is drastically simpler. For all I know this could inhibit Rust's future ability to do even more powerful things with types, but AIUI this scheme has the advantage of being actually decidable given the extensions to HM that we would require in the current language.
I ain't a type theorist though, so take this as hearsay. :)
Strictly speaking, I think almost no extant languages, and certainly no mainstream ones, use pure HM, but many take it as a starting point. Certainly, HM has no notion of ML modules, or type classes, or record types, or lifetimes. Nevertheless many languages using those things use HM as a starting point.
I'm curious (and a bit skeptical) of your claim that the scheme is "drastically simpler" than HM. HM is a beautifully simple design, which can be expressed (abstractly) in just a couple of lines.
"This scheme simplifies the code of the type inferencer dramatically and (I think) helps to meet our intutions (as I will explain). It is however somewhat less flexible than the existing inference scheme, though all of rustc and all the libraries compile without any changes."