If this involves the Creative Cloud services, you can have your cake and eat it too. You are allowed to have two machines with enabled installations and the two machines can have different platforms.... Mac and Windows PC.
Just install the desktop manager on the new machine like you did for the Mac.
Learn how to download your Adobe Creative Cloud apps
Since you mention having an old Mac.... if it is really old then you might not be talking about the Creative Cloud services, but instead one of the Creative Suite ensembles... in that case you are still allowed to have two activated installations, but in this case they have to be of the same platform, Mac or Windows PC.