A follow up to my own post (via @jimsz link)
It says on the United States Patent and Trademark Office website that Jake filed for a "Standard Character Mark". And what is that you ask? (because I sure did!)
From:
https://www.l4sb.com/blog/standard-character-marks-vs-stylized-logos/
The Standard Character Mark (also known as a word mark) is used to register words, letters, numbers or any combination thereof. However it does not lay claim to any particular font style, size, color or design element. In other words, a single word mark protects the phrase regardless of how the words are displayed.
So yeah, the word "Inktober" has been trademarked. I note that there isn't anything about the logotype. It's possible that Jake is protecting that via copyright. Or that the logotype is protected under the umbrella of the "Inktober" trademark.