I moved my Steam games to another computer, but it still wants to update the games already update on the old computer. Did I miss a file to verify updated games?
It's possible you missed a file, but Steam wouldn't know that. It's just asking you to update because that's what it's programmed to do. It's done this way to account for things like corrupt files, files you missed while moving, or any other unforeseeable problems.
I suggest updating, it shouldn't take too long if you've actually got all the files.
Steam install, update and manage your games for you. You said that you moved your games to an other computer. Maybe steam just want to be sure the configuration is OK with your new material? I would recommend to do these updates in order to be sure your games are installed properly and ready to play.
Steam also updates your games on a regular time basis just for the cloud to sync again. Since pretty much of the saved data of your game is cloud-managed and not local anymore, you want steam to update those precious informations to continue playing where you left on an other computer.
As long as you moved the entire Steam directory, you are fine.
Personal experience: I reinstalled windows, and moved my entire steam directory from my old drive to the new. When I opened Steam for the first time, almost all of my games said an update was required. All I had to do was run each game once, and it recognized the existing files and removed the update notification.
In short, run each game once. The update message goes away.