I think it rather means that the search time was short enough that neither search tree got deep enough to form advantageous moves. (When I check the detailed output, it seems that the asm.js version visits at least 2x as many nodes as the un-optimized version, independent of Time-per-turn)

I see the same, if I set it to 50ms or 100ms they ususally draw. At 500ms asm.js absolutely dominates.

That doesn't mean anything, asm.js only increases the amount of positions searched. If it searched more positions and still lost it means it either searched the same depth on average (which means the extra computational power did not finish a deeper search) or it just happened to lose despite it. See if it's searching more positions on average.