No, to hunt all game, including big game, he needs either the type 073 or 074 All Game License.The "weapon" licenses are supplemental licenses for residents.
If he wants to take antlerless deer during the gun season on the Special Season hunt, he will need a Type 94 permit. He also would need the appropriate permits to small game or waterfowl hunt on a WMA. If he hunts migratory birds, he will need a migratory bird permit even if he has one for his home state. The federal duck stamp is good in all states.
And, if born after Jan. 1 of 1969, he must be hunter safety certified.