is it working?
 

I recently acquired DW from Steam.

I am running it on Windows 7.

I just installed--I think--LWAMI mod 3.11 but, when I launch the game, nothing seems to be changed. Same splash screens and no indication of anything different. How can I tell if it is installed properly and working?

splash screens are installed separately via JSGME. Having an aftermarket splash loaded does not mean you are running a mod, nor does having the stock splash mean you are not running a mod.

There are lots of ways to see what database is active, but I would imagine the easiest is to go to the USNI and load a platform that doesn't exist in stock DW. E.g., just off the top of my head, the Astute SSN for the UK. I don't think USNI can reference a model unless the proper database is active.

Before we expanded the USNI I used to say to shoot an SS-N-27ASM and see if it sped up (stock) or fired a 2nd stage (LWAMI).