From the OSP main page:
"If the operating system vendor/community provides open-vm-tools, then it is recommended to use open-vm-tools that are provided by vendor/community. VMware will not provide OSPs for operating system where open-vm-tools are available."
So VMware decided to cut off support for Ubuntu's OSP for releases after 12.04 because open-vm-tools is available through the regular Ubuntu repository. I see open-vm-tools is also available for 12.04 from the Ubuntu repository.
Also, your post quoted the page as saying "Ubuntu Linux (LTS releases only) 12.04 and higher" but I see they changed the wording to "8.04 to 12.04." I'd been regularly watching that page for updates but only just now noticed the difference. It's not clear when they changed it. I'm glad you quoted that line in your original post, so I know I hadn't been misreading the page all this time.