Depends on the game.
If it is just Renpy VN's you can just copy the folders and most games on here that don't require an install and run straight off the folder.
For Steam games whether you install the HDD with all the installed games to the new computer or copy the files to the new Hard drive, you can just tell steam to install the game and as long as you point steam to the same directory, it will take a seconds for steam to find and recognize the game as installed without waiting minutes to download and reinstall since it detects the files. I think if you just set the installed directory to the one you copied over, Steam will recognize it without having to tell it to install.
In the same vain other non-steam games work the same way if you install games in the same directory as the copied files, it will skip files already there and will take seconds to reinstall.
Some installed games keep their save files in documents folder on windows machines so make sure you copy that too. I would just clone the whole hard drive on your laptop just in case you miss something.
If you don't know where the save files are you can usually google "where are my save files for X game."
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Probable don't have to go that far, copying documents and the game install directory should be enough.