Not necessarily. If it’s using the standard reCaptcha, there’s two words. One of them is “known” to the system and spelling that one wrong will fail. The other one is either only partially known or is unknown, and it’s gathering data. If you spell that one closely enough, it’ll still pass you.
I’m pretty sure that they sometimes combine portions of two unrelated snippets to help figure out where the letter breaks are. Like, if the system knows that one image means “canonical” and one means “barmy”, it might randomly give different chunks concatenated together to people.
When you tell it that the word you see is “barmonical”, it knows where those two letter breaks in the original words are.
The last bit is total speculation based on my experience seeing reCaptchas, and on some basic knowledge of how such systems are designed. It does look like it could explain all or almost all the “words” you have.
I collected the words from those presented in the Captcha test used to prove the user is a human. I’ve done this many times and just assumed they were random letters, not words. When I clicked the help option offered on the Captcha box, it lead to the text I quoted in the OP, stating it was from old text, and referencing the NY times. Each of the words I’ve listed are words that passed the Captcha test and allowed access to the the site, registering, etc. I assumed these words are the ones they are referring to as “old text” (the words I’ve quoted above). I’m curious as to whether there are old, abandoned words.