Take it this is Rhino under the hood somewhere, or has someone written a new js engine?
Also for anyone interested in an easy way to use the JVM for other languages, check out crudzilla.com . It is primarily for web development but has basic editor for other development work.
asm.js isn't relevant here at all.
DynJS could also support asm.js in addition to JavaScript, but that has almost nothing to do with JIT-ing JavaScript applications.
Although with invokedynamic, the JVM's object system ends up being remarkably close to that of a dynamic language. This is best seen in JRuby.