Yes, you are correct. What I wanted to say is that webassembly is a continuation in that direction. At the time asm.js was ideated the alternative were browser

Yes, you are correct. What I wanted to say is that webassembly is a continuation in that direction. At the time asm.js was ideated the alternative were browser plugins like NaCl, Flash, or Java. The problem with asm.js is that the requirement to be a subset of javascript meant that some optimizations were impossible. wasm is another step in that direction.