I decided to take a crack at assembly the other day, and I\'ve been playing around with really basic things like printing stuff from argv to stdout. I found this great list
RCX, along with R11, is used by the syscall instruction, being immediately destroyed by it. Thus these registers are not only not saved after syscall, but they can't even be used for parameter passing. Thus R10 was chosen to replace unusable RCX to pass fourth parameter.
See also this answer for a bit more information on how syscall uses these registers.
Reference: Intel's Instruction Set Reference, look for SYSCALL.