It isn't really type inference. Each closure gets a unique type. Rather it's an automatic decision of what traits (think roughly "superclasses" I guess if you aren't familiar with traits/typeclasses) to implement for that type.
If anything it's closer to SFINAE in C++ where it tries to implement methods but then doesn't consider it an error if it fails. Then infers type-classes based on the outcome of the SFINAE process. Or the macro analogy another poster made isn't bad (with the caveat that it's a type system aware macro - which at least in rust is strange).