Games with no gun action? Hm, someone needs to go through his catalogue of adventure games, methinks...
Try, I don't know, any Cyan Worlds or Sierra title from the old Roberta Williams days. Try city builders or even the occasional and ultra-rare stock-exchange simulator (yes, those exist). Play the recent Shadowgate remake, seeing as bow-and-arrow action is extremely directed and mostly optional, as is sword-and-shield gameplay. Try Legend of Grimrock 1 and 2, etc.
Heck, there's a ton. At least the OP didn't go for the tired "Ugh, all we do in games is shoot at things!" excuse.