@Eventenkate
Files of your game aren't kept in the cloud. These files are only into your old computer so you must move these files to this new computer.
How to do this:
You need to pack the "saves" and Tray folders using WinRar program on your old computer. These folders can be found in Documents / Electronic Arts / The Sim4. The Sims4 folder is your game folder.
You can save such packed folders on PenDrive - or send it via e-mail to your own address. You send this e-mail to your e-mail address and attach the packed folders. Because they have a large volume you will need to use Google Drive and have a Gmail email address.
Download these packed folders from Pendrive. or move these packaged from mail to some place on your new computer.
These folders you first unpack and then paste into a new game folder in Documents on your new computer. Of course, before that, you have to delete new folders with the same names that were created there after installation.
I don't work for EA