"하는 거" is a spoken form of "하는 것" meaning "doing something", and "하는 게" is short for "하는 것+이( = subject marker)" meaning "doing something is...". \^o^/

게 is 거(which is informal speaking form of 것)+이.

게 is 거(which is informal speaking form of 것)+이.

하는 거 & 하는 게