PGP (including GPG) 'armoring' is not encryption. Encryption prevents unauthorized use of data (formally, provides confidentiality) by making it unreadable in a way that can only be reversed by someone who has the secret key. Armoring is a simple process (mostly base64, although not the same base64 used by uuencode) that can be easily reversed by anybody who reads the specification. Armoring looks like text while unarmored (binary) data looks like garbage to a person who uses inappropriate tools like
cat or a text editor, but they are equally readable by someone competent.
In particular, a signed but not encrypted PGP message can be read by anyone competent, whether it is armored or not. A PGP public key ditto. An encrypted PGP message can only be read by someone who has the key -- depending on the way the message was encrypted this could be a private key, a passphrase, or both -- and again this is the same whether armored or not. A PGP private key is always encrypted, and can only be fully read by someone with the (KEK) key (in this case, always a passphrase); however, the public part of a private key can still be read by anyone competent, again regardless of armor.
The purpose of armor is to assist in correct processing. In the days when PGP was created to be used for email, most email systems could only handle text and would damage, mangle, or entirely discard binary data. For PGP messages, and keyblocks, which are inherently binary, to be successfully transmitted, they were 'armored' into textual form, and un-armored when received and processed. Nowadays nearly all email systems do handle binary data and this is rarely needed, but armoring still can be useful if you want to process the data using tools designed for text, for example cut-and-paste, or as your quote suggests a webpage (HTML handles text but not binary). It also has the advantage of being easily recognized by people without any use of tools.