Yep, Grim Fandango, Monkey Island, etc... (Psychonauts is by Tim Schafer too)
Now my hands are on Full Throttle!
From 1995 (and thanks ScummVM!)
This game uses (obviously) the Scumm engine and the inventory and the actions are hidden on the screen: a with a long left click on an object a menu appears with actions (look, talk, punch or action with hands, kick) and with a right click you can view your inventory.
I'm stuck at the dump, let's see if I can do something.