Who to contact there is often unclear. Inventor Relations in another group worth contacting if the out-licensing group is unresponsive. If you're lucky, the licensing dept. will be able to quickly ascertain if their firm has retained the rights for the game in question. If you're lucky, they haven't, but can provide you with the name of the creator, or agent, who currently holds those rights. Ma y game contracts require an annual royalty payment.
Some contracts are for a specific period of time and have expired.
You're usually unlucky if the firm has retained the rights. People there will need to decide if they have any further interest in the game which would preclude them from licensing it to you. This could take months. Further, they may have restrictions in their contract with the inventor that prevents them from so doing without the inventor's approval and significant money changing hands even if they're so inclined. This is wise in any event because you need to know if the game's title is clear or if someone else is now using it.