How Does One Transfer A Steam Game? [duplicate]

I have a failure to transfer my game from one HDD to another, and one PC to another. I copied the entire Skyrim folder from one HDD to another. And told where to find it also. Steam did a huge check of my HDD.

But it ended up downloading most of the files anyway. It took a week to download Dawnguard, Hearthfire, and Dragonborn files along with my Hi-Res textures.

I did ask about it in chat. But I feel this could help me or somebody else.

This is the screen I am looking at after transferring my entire hard drive to to new one. Steam downloaded my games, including Skyrim even though my Skyrim data folder had all the data files for Dawnguard, Hearthfire, Hi-Res and Dragonborn.

I have my copied files and have got rid of everything not steam related. I just have my DLCs and they include my hires files.

This is what it looks like.

But I still get this :

What could be causing this? How can I rectify? And in future when one is migrating to a new PC, how can this be avoided?

EDIT::::::::::::::::: Removed everything : Here is how it looks :

Still the prompt as before Steam Error 15

(Side Note : I transferred all my Origin games just by copy/pasting. This really is not nice.)

EDIT 2 :::::::::::::::::::::

And one more EDIT

I tried getting game cache up to speed, but this is prompt I am getting. But I played the game, it was working, I could pick out my character and all, and escape from Helgen.

EDITED 3 :::::::::::::::::

How does one transfer a Steam game? A game that is heavily modded, will the backup a Steam Game option suffice?