How to backup running KVM guests, when using qcow2 disks and host system does not use a LVM? Is it even possible without guest shutdown?
Yes, all you need to do is take a snapshot of the disks while the VM is running and copy the backing image while the VM is running off the snapshot.
To get rid of the snapshot live, you need to have a fresh version of libvirt and qemu, and you need to either execute
virsh blockcommit or
virsh blockpull, depending on whether you want the snapshot merged with the base image, or the base merged into the snapshot.
For syntax details, libvirt has a great wiki