Is there a medical definition of "immuncompromised"? would someone with a neutrophil count of 14.1 x10^9 or myeloproliferative disorder qualify?

Immunocompromised: Is when the immune system is not working at optimum as after chemotherapy, after a sickness, being given steroid, immunoproliferative with nonfunctional white cells, in diabetes, in renal failure, in bone marrow depression, people with chronic diseases as in sle, cancer, etc. I think you get the idea, it's not always the count, it's the function.

Yes: Immunocompromised means that you have an impaired immune system but the impairment may be different from one individual to another. People with myeloproliferative disorder can indeed be immune- compromised due to diminished and/or defective number of immune cells (mostly lymphocytes) produced . Low but not high neutrophils also increases the risk to get seriously ill from even minor infections.