Apple offers iCloud Backup for iPhones and iPads but not for Mac computers.
You can sync some data, as described below, with iCloud. If the syncing options are on in both Macs, data deleted from one will be deleted from both and from iCloud.
However, if you erase the old Mac using the procedure described in What to do before you sell, give away, trade in, or recycle your Mac - Apple Support that will not affect the other Mac or iCloud.
It is possible to sync data from a Mac to iCloud if you turn on those options (e.g., iCloud Photos, iCloud Drive including the Desktop & Documents option). Syncing has some of the benefits of a backup (and the benefit of being offsite) but is not the same as a backup. Major differences include the fact that not everything on your Mac can be synced and the fact that if you delete something, accidentally or otherwise, there is only a limited time period (30 days in most cases) during which it can be recovered.
Also see the Apple article: How to back up your Mac - Official Apple Support
And more information on syncing in:
Set up and use iCloud Photos - Apple Support
and
Access and manage your files in iCloud Drive - Apple Support
and
Add your Desktop and Documents files to iCloud Drive - Apple Support
