Confusion regarding root locus. Open loop or close loop?
The answer is relatively simple: 


From stability considerations we know that the poles of the closed-loop function H(s)=N(s)/D(s) must not enter the right side of the complex s-plane.
The poles of the closed-loop function are identical to the roots (zeros) of the denominator D(s) (which is identical to the characteristic polynominal of the system).
Therefore, the root locus analysis is performed for the closed-loop system.


Comment (EDIT): I think, the wording of the quoted text is a bit confusing (..."root locus of an open-loop transfer function"...). For my opinion it should read: ...the root locus for a transfer function H(s) under full negative feedback for different proportional gain values K"...