An "easement by necessity" is very narrowly construed, and follows the property (in general this form of easement is frowned upon and only exists as long as necessary).
However, it is not limited to the actual owner of record. If the owner is abusing the right of access, or is causing "waste" to your property (deemed the "servient parcel" for these purposes, the property enjoying the right of way is deemed the "dominant parcel"), you can sue the servient landowner for damages.
Usually the game warden is not involved in this kind of dispute - other than the fact that these properties are being used for hunting, they have no jurisdiction here, and are not involved - this is a civil matter and would be resolved in civil court (that being said, if you were to take "self help" measures and blockade the road, or cut ditches, place rocks, etc. - expect a civil suit with money damages being levied against you promptly).
I would recommend that you consider reaching a road use agreement with the property owner, promptly. If you cannot negotiate one directly, I would recommend contacting the local bar association and asking for referrals to mediators - often a third party neutral can help you reach a mutually agreeable resolution to come up with a way to address both their need for access, as well as your need for maintenance, safety, and minimal impact on your property.