Access to DOM APIs isn't part of the MVP, but it is listed as a high-level goal[1] and is specced as a future feature[2].
[1] https://github.com/WebAssembly/design/blob/master/HighLevelG... [2] https://github.com/WebAssembly/design/blob/master/GC.md
[1] https://github.com/WebAssembly/design/blob/master/HighLevelG... [2] https://github.com/WebAssembly/design/blob/master/GC.md
https://github.com/lukewagner/polyfill-prototype-1
PoC mentioned in the wasm FAQ.
I feel like there may be enough internal pressure from groups in Apple, Google and Microsoft to get DOM integration available, so that they can experiment with compiling the likes of Swift, Dart and C# to it, that it will become a priority once the MVP has shipped.