From every thing I've seen the system is a Lua code compiled down Assembly (ASM.js?) running on top off JavaScript with a minimalist HTML5 library.
Thats a lot of technical mobojumble. In plain English it means: it's extremely effecent. But it requires a modern brower to work right.
You might be able to get around some of the HTML5 limitations by adding Modernizr (sp?) or some other JavaScript library. Modernizr tries to fill in the gaps that older browser don't support. As some other people said the PSP is very low power.
To work right someone would have to make a native compiler. Which is very fesible due to low resourse TIC-80 takes.