I read from here pag. 209
The residue ring of an *-ring is an *-ring itself. Hence follows that if R is a closed *-subring of the ring of operators in Hilbert space, then any its residue ring can be imbedded into the ring of operators in Hilbert space
and from wiki
.. C*-algebras since it established the possibility of considering a C*-algebra as an abstract algebraic entity without reference to particular realizations as an operator algebra.
Ok, but if Von Neumann he needed to use ring of operator why we need to abstract its work to avoid to use an operator algebra?
I know that quantum mechanics formalism use Von Neumann approach in many aspects, not Gelfand-Naimark that I prefer instead.