I have no idea what people are talking about here (web bytecode and web assembly doesn't make any sense to me... thought the latter probably is intended to mean asm.js which is just a subset of js that allows for optimization based on the limitation of this subset).
They compiled C/C++-code using Clang (or possible gcc w/dragonegg, but my guess is Clang 3.2 as that's the supported compiler for emscripten) to LLVM bytecode and then to JS/HTML5 using emscripten, which is aware of asm.js and optimizes for it.
Mozilla (which Kripken is also highly involved with) are behind asm.js and is supported in the latest nightly of firefox (supposedly giving speeds to within 2x of native code, which is damn impressive), and the guy behind emscripten (again, Kripken) works for Mozilla.
I'm don't know to what extend emscripten is part of Mozilla or his own personal project.
So can you add some dynamic code into asm.js and expect same performance? Asm.js is an assembly that looks like JavaScript for compatibility and readability.
No, asm.js code that parses successfully is compiled ahead of time. It is a strict subset of the JavaScript programming language. If you use parts other than the subset, it will fail to parse as valid asm.js code and revert to the interpreter/JITs.
Minified Javascript does not operate on an enormous buffer of bytes, such that you get seven and eight digit numbers flying everywhere. It's still easier to understand and manipulate than ASM.
asm.js isn't just an evocative name, it's a reasonable description... it's assembly in Javascript.