Thought I'd share this with you, even though it's not a game, and it's not even about Indy himself! But the author hsa made a sterling attempt to get close to the atmosphere, using some supernatural (religeous) twists on the Indy-theme to make it different (enough). So here's where you can find it:
http://www.podiobooks.com/title/ancient-rising-1 (http://www.podiobooks.com/title/ancient-rising-1)
(BTW you did realise I was writing about an audiobook, right?)
And yes, the warning about the synthetic voice starting at chapter 12 is very prudent (and fortunately not needed fo most books there, being fully narrated by humans), but still worth a listen!