What kind of doctor sees somebody for cervical myelopathy?

Neurosurgeon: Neurosurgeon, spine surgeon, neurologist.

Spine surgeon: Usually it is a spine surgeon (orthopedic or neurological spine surgeon). Sometimes a rehabilitation physician (physiatrist) will care for myelopathy. Myelopathy due to spinal cord compression is usually best treated by surgery unless the symptoms are very mild and stable (not worsening), or other medical conditions make surgery too risky.

Several: There are several specialists that may be involved from a neurologist who may diagnose this and then refer to a spine surgeon ( orthopaedic or neurosurgical ) for definitive treatment to a physiatrist who may get involved in post op rehabilitation or management if there are reasons not to operate along with a neurologist then for the same reason.