took my clutch off today and notice some play iin the shaft in and out not sure if this is right or not? its not alot but its some

 

I have a 06' eiger 400 semi auto, my bike began to slip after overheating in the mudd. I stopped to allow it to cool then tried to take off my bike went into gear but wouldnt move. When I took it apart and my clutch shaft did have minimal movement. I beleave that it is suppose to move slightly.
I replaced the primary clutch shoes and put it all back together and my bike is doing the same thing it had done before I replaced the shoes. Does anyone know if the centrifgual clutch would have something to do with the bike going into gear but not moving?