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Yes, LXC (the author meant LXC for "LXE" I think; the ProxMox appliance believe currently uses KVM and LXC (Proxmox previously used OpenVZ for containers, but that (OpenVZ) has lost much of its Linux OS support)) has definitely been around longer than Docker. Docker originally used LXC as its container tech.

Yes, the author is specifically refering to KVM (https://en.wikipedia.org/wiki/Kernel-based_Virtual_Machine) which was merged into the Linux kernel in 2007.

Whereas Docker (https://en.wikipedia.org/wiki/Docker_(software)) was first released in 2013.

Believe that the author was actually specifically referring to LXC (misnamed as "LXE" in the article), with his Docker reference.

Linux containers have been around for decades. Docker made the concept popular and more approachable.

A quick wikipedia search says Solaris Containers date back to 2004 but Linux Containers "only" 2008. Unless you're lumping chroot jails under the "containers" header.