According to the docs, Quintus does support mouse and touch input.

On my PC, the demo is controlled by keyboard only. Presumably, they wanted to make the code as small as possible so they didn't put touch controls in.

http://html5quintus.com/quintus/docs/quintus_input.html

Check out some more examples that use the engine and all run on mobile here: http://mh5gd.com/ (all but the first are built on an earlier version of Quintus from the book)