To say this game is played as a sport is some sort of a joke that i don't even want to get into.
Imagine trying to say this in basketball. "So people with impaired movement in their feet should have to suffer the consequences of not being quick enough to play defense?"
Yes. They should. Sorry
Uh.. No, they shouldn't. Sorry.
In basketball those who are movement impaired do have compensations. Many tournaments have been hosted for those with the inability to walk.
Secondly, clicking is not a skill. It feels like you're trying to sound sophisticated in some way by acknowledging the fact that there must be some sort of physical skill, and that's not the case in a virtual game.
Let's pretend this is a "sports" game. (which is like saying chess is a sport granted you use a speed timer.) You're pretty much saying moving one piece to a certain location requires skill, and someone without arms isn't skilled enough to do it, and that's ultimately their own fault. No, that's not how it works, and no that is not their fault.
Clicking 10x super fast in a quarter of a second is not skill. It has nothing to do with reaction time, and therefore it shouldn't be required.