TMI is certainly going to use more resources than Sam & Max because it has higher levels of modelled detail, higher-resolution textures, and more special effects such as depth of field blurring and special textures.
Of course, most of these should be disabled when you lower the detail in the options. Are you saying it won't run well even if you do that?
Assuming you've been to NVIDIA's website and downloaded the latest drivers for your card, I can't think of anything to suggest beyond grabbing a better graphics card. Your other hardware seems fine, but the 8600 GT is getting on a bit seeing as it heils from 2006 and even then was considered a strictly low/medium-range card.
You would be able to get something more than adequate for running games well beyond TMI for ~£100, half that if TMI is pretty much as far as your gaming interest goes.