@diakanos For the install process, yes, this is true for any game the EA App supports. You can simply sign into your account and download it on the new computer without transferring anything from the old one.
As far as saves are concerned, different games store them in different folders, but you should have something on your old laptop that you can transfer to the new one. Sims 4 saves are in Documents > Electronic Arts, and some other EA games also create folders in Documents. Others store save data here:
C:\Users\your username\Saved Games\[studio]\[game]
And a few older ones store save data in the game's program files. If you can't find the data, google should be able to tell you where to look.