There's a general mismatch between popular conceptions of type system expressiveness and actual type system capabilities. Elm has a very simple type system. In fact it is very close to having among the simplest type systems in any statically typed programming language (the only things that really set it apart are tagged union types and record types). For example Java has a much more expressive type system than Elm in many ways. What perhaps makes Elm's type system seem advanced is that the runtime essentially never violates the guarantees of its type system, unlike Java (depending on your opinion of unchecked exceptions).
Haskell has a much more expressive type system than Elm, but still lags behind Typescript unless you turn on a truly gargantuan number of extensions.
It's also a bit weird to compare the languages because Typescript has a very different typing regimen than Haskell or Elm. Typescript is entirely structural while Haskell is almost entirely nominal and Elm is mostly nominal (with the exception of records).
Typescript has an extremely expressive type system. It is in fact so expressive I'm amazed that it's gotten so much adoption when languages like Haskell are still considered "advanced." I suspect it has to do with the semantics of the languages rather than the type systems.