You can clone your SSD to another one and it will be exactly like the SSD you have. I did that to clone my old HDD to a new SSD a couple of years ago. I used Samsung's Data Migration tool, that people say is the best one to use.
https://www.samsung.com/semiconductor/global.semi.static/Samsung_SSD_Data_Migration_User_Manual_(ENG)_v.3.1.pdf
I don't think just copying and pasting the installed game would work since I think it places files in Windows registry and maybe in other places as well.