Conclusions, based largely on the comments and hence provided as a community wiki answer so that this question ends up with an actual answer:
It's likely that Microsoft mean that the separate tasks of (i) interpreting and/or running; and (ii) compiling occur in parallel. It's probable that they've applied technology like Sun's old HotSpot JVM so that the Javascript virtual machine interprets code at the first instance because it can start doing that instantly. It also JIT compiles any code that appears to be used sufficiently frequently for doing so to be a benefit. It may even have different levels of compiler optimisation that it slowly dials up. In that case it may be using multiple cores to interpret or run one fragment of code while also compiling arbitrarily many others, or even while recompiling and better optimising the same piece of code that is being run.
However, it's also possible on a technical level that you could perform static analysis to determine when callbacks are mutually independent in terms of state, and allow those callbacks to execute in parallel if the triggering events prompted them to do so. In that way a Javascript virtual machine could actually interpret/run code in parallel without affecting the semantically serial nature of the language. Such a system would be logically similar to the operation of superscalar CPUs, albeit at a much greater remove and with significantly greater complexity.