In typical jQuery usage, the dollar sign is used as an abbreviation to indicate the call to a jQuery function. As you rightly point out, MooTools uses the same abbreviation and so using both libraries on the same project has the potential for conflict.
However, Yoshki doesn’t use the dollar sign abbreviation when calling jQuery functions and uses the full “jQuery” call instead. This removes all conflict with MooTools, and to confirm this, we have several websites with this exact setup with no issues.