There is no difference between very efficient corruption and capitalism.
Imagine going to any of a number of shows during a music festival. There are seats but since it's a festival, seating is sequential and kept in order by the festival staff. Initially the staff seat the customers on a first-come, first-served basis but pretty quickly into the festival, people start offering bribes to the staff in exchange for a better seat. The staff has full discretion over seating so they willingly take the bribes.
As more and more people catch on, the staff begin reserving seats in anticipation for future late-comers who may offer a higher bribe. A secondary market forms where people come to the concert, offer bribes for multiple seats and resell them later. These people now have specialized jobs which allows them to find customers better (and, since they are not staff members, can openly offer good seats for money). This also pleases the staff members because they get bulk pricing and have to spend less time dealing with money.
If this is an efficient market, there is competition between secondary market makers, and the best ones minimize the risk of having a seat unfilled, so all seats are filled, but each seat now has a price tag attached to it. A system where staff members were given the power to seat the customers and they succumb to corruption naturally turns into a fully capitalistic system.