Indiana Jones and the Fate of Atlantis
Indiana Jones and the Fate of Atlantis is a point and click adventure by LucasArts, and only one of many, many Indiana Jones games released.
Accuracy again, is low, but by the time this game was released, the tropes that you expect from Indiana Jones and modern media are fully present in games including archaeology. Specific artifacts and cultures are fully integrated and represented, and the player is encouraged to think archaeologically and to reference archaeological sites to solve puzzles.
Unfortunately, this game also set pseudoarchaeology as the prime narrative driver. From here on out there is almost always a supernatural or mystical influence, and ancient peoples are almost always connected to lost knowledge or alien influences.