jeff.pace is dead on. I just opened a web site that checks for touch events ("ontouchstart" in window || false). On my laptop, which has problems with mouse-events in Chrome and Firefox, it opens the mobile version of the web site on these two browsers, but on IE it opens the regular web site. And the ArcGIS JS API mouse-events only works in IE for me.
My problem is probably that I have installed some Microsoft SDK (Surface or something) that sets my laptop as "touch supported".
I also have problems with mouse-events in some Dojo dijits (dropdown button, resizable content pane etc.), in the same browsers.
So I bet there is a check for "touch support" in the ArcGIS API for JavaScript (and dojo). And the solution is probably to also check for mouse-support, and allow for mouse-events.