I can't seem to find a list of cards supported for Gray matter.

I have a brand new i5 2500K 8GB 1TB HDD desktop with an AMD Radeon HD 6670 graphics card.

Is this sufficient?
I have no idea what most new adventure/mystery PC games require

Please help!

The card should be able to handle the game, but make sure you don't ramp up the graphics settings.

I played the game on my laptop which has an IGP very similar in specs to your card.

Edit -

If you card has GDDR5 memory (as opposed to GDDR3) you're even better off - those flavors have a much higher bandwidth.

AMD Radeon™ HD 6670 Graphics

AMD Radeon™ HD 6670 GPU Feature Summary

800 MHz engine clock
512MB-1GB GDDR5 memory
1000 MHz memory clock (4.0 Gbps GDDR5)
64 GB/s memory bandwidth
768 GFLOPS Single Precision compute power
TeraScale 2 Unified Processing Architecture
480 Stream Processing Units
24 Texture Units
32 Z/Stencil ROP Units
8 Color ROP Units
128-bit GDDR5 memory interface

^^That was a bit of the info from the AMD site.
There's more but it was mostly with DirectX and Eyefinity stuff.

You've got the GDDR5 model - you're good to go.