"It has effectively the same function as a proxy" isn't the same thing as "it's not actually a VPN".
One could argue you're not really using the tech to its fullest advantage, but the underlying tech is still a VPN. It's just a VPN that's being used as a proxy. You're still using the same VPN protocols that could be used in production for conventional site-to-site or host-to-network VPN configurations.
Regardless, you're the one who brought up commercial VPNs; when using OpenVPN to create a tunnel between a VPS and home server(s), it seems like it's being used exactly to "create private communication between multiple clients". Even by your definition that should be a VPN, right?