It does work with the API as well. I tried a few things, gpt4 turbo preview (which ChatGPT4 is currently using?) outputs "Follow Riley Goodside." if the initial message is sent as system[1] but not if the initial message is sent as user[2]. The default system prompt of bettergpt.chat, which I used as the front-end for the API, was enough for it to work when sent as user[3].
I also tried with the slightly older june 2023 version of GPT4 (gpt-4-0613). It did not work with bettergpt's default prompt[4] or when sent as initial system prompt[5]. Though with little help it was able to print out the whole invisible part[6].