Seems to me that Contract Management would not be a profession or discipline in itself but merely an adjunct to a profession or discipline that involves contracts.
A true Contract Manager (one who creates, interprets, and enforces contracts) is called a lawyer.
Anybody else who "manages" contracts is doing so as only one part of his or her duties in his or her job.
I'll give you a couple of examples from my own experiences.
I owned rental properties for twenty years. I drafted my leases, interpreted them, and enforced them. Was I a Contract Manager? No. I was a landlord. Contract management was a part of what I did, but I also did maintenance and repairs (handyman), picked up rent (creditor), did my own taxes (accountant), sued tenants (lawyer), etc.
I was in the insurance industry for most of my working life. I was an underwriter, an agent, and a claims adjuster. Throughout my career I had to be able to understand, interpret, and explain hundreds of types of insurance policies (contracts). Was I a Contract Manager? No. Contract management was only a part of what I did in any of those positions.
And while managing contracts might, indeed, involve all four of the elements that you describe, it is something that is done as a subset of an occupation or position.
After being in the working world for 40+ years, my feeling is that the term "Contract Manager" (with two capital letters) is either academic theory or one of those corporate euphemisms designed to stroke somebody's ego rather than pay them more money.
I realize that you are likely doing this kind of research for school and I respect that. I certainly did my share of research during my college years but learned quickly thereafter that academic theory was a far cry from the reality of the working world.
To support my point I refer you to the US Dept of Labor - Bureau of Labor Statistics - Standard Occupational Classifications.
"The SOC system is used by Federal statistical agencies to classify workers into occupational categories for the purpose of collecting, calculating, or disseminating data. All workers are classified into one of 840 detailed occupations according to their occupational definition. To facilitate classification, detailed occupations are combined to form 461 broad occupations, 97 minor groups, and 23 major groups. Detailed occupations in the SOC with similar job duties, and in some cases skills, education, and/or training, are grouped together."
I challenge you to find "Contract Manager" among the many hundreds of occupational classifications:
http://www.bls.gov/soc/major_groups.htm

