Alessandro - To confirm - are you logging into AGS using the same Account you used on your old PC? If so, any games you have purchased from our store should download once you've logged in.
Any other games you had on your old PC (not purchased from us) will not transfer to your new PC since we don't have any ability to manage those games.
If you are using the same account, please email me at adam@polycade.com so I can have our engineers look into it. In that email, please share your new PC's MAC ID, old PC's MAC ID (if you don't have this, please share your IP address), and the email address on your account. I'll also refund that duplicate purchase for you.