I have created a new issue on Let’s Encrypt GitHub to clarify Windows XP support. I also found the likely problem why Windows XP doesn’t accept the Let’s Encrypt intermediate certificate. See https://github.com/letsencrypt/letsencrypt/issues/1660
EDIT: The Let’s Encrypt FAQ has been updated for the time being with “Most platforms that trust that root should trust Let’s Encrypt certs. One notable exception is Windows XP, which currently doesn’t accept our intermediate.”
All hope is not lost, Josh Aas was assigned to the issue and it may be possible to create a new compatible intermediate certificate.