Why does the cloud have my photos when I haven't saved them there?
You are confusing your iCloud Backup with iCloud Photo Library.

iCloud Backup by default makes a copy of your whole iOS device, in case you have a problem with it (you erase something by mistake, it gets stolen, lost, damaged) to be able to restore it to the last available backup.

You can selectively remove different data from the backup, that —of course— won't be available to restore later on.

iCloud Photo Library is a different service: it will allow you to upload all your full size pictures to iCloud, save a smaller sized copy on your device to save space (if you set it that way) and sync them between different devices.

So "the cloud" has a copy of your whole phone for backup purposes because you activated iCloud backup. You can deactivate it and erase it, —I would advice to make a local backup regularly with iTunes in that case— or leave out only your pictures from the iCloud Backup, by deselecting the "Photo Library" item on the "Manage Storage" settings under iCloud Backup (shown in your screen capture).