Replacing a dimmer out of a 2 gang switch
Its very common to split or chain light circuits in parallel. Outlets too.

If you wanted to be quick about it, turn off circuit breaker, cut and strip those two wires that are comming out of the dimmer, and screw them to the brass terminals on the new switch. Btw, you can remove the green screw since its not used in this class of wiring. I would take re-tighten any wire nut splices so that there is no copper wire showing, Looks like the one in the picture needs to be redone. 

In some areas, the feed wires are not labeled, so when I see one like this white wire used as a feed (power, instead of common) I mark it with a black marker.

btw, they do make led lights that are compatible with dimmers.