I don't know why so many people use google analytics lately, i think it's hard to spot what's better.
My search terms would be like this:

http://tiny.cc/sn37b

I doubt anyone really searches for "unreal development kit". They usually use "udk" so you get way more requests.

Also for unity 3d, i usually never use unity 3d as term, just unity. The engine itself isn't called "Unity 3D". Just the website (i forgot why it was like this). The engine is just called Unity. (Many people don't know that actually).

There is (or was) another engine called unity3d which had nothing to do with UT (unity technologies).

As for 3dgs, i often use gamestudio and when i first tried to find an engine many years ago, i used gamestudio as term as well, and found 3dgs. So you get more counts there too.

Anyway, i really doubt 3dgs is dying. It has a lot of advantages for newcomers and you still keep hearing about it (and i'm saying this as unity user :P).