Etymology of Kowtow in English

I was chatting to a friend at the weekend about foreign loanwords in English. We were talking about how there are (relatively) few Japanese words and, having just encountered it in Level 18, I mentioned kowtow:

WK Explanation
“Tap your head against the floor to show your subservient respect by doing the kowtow bow. This is the most respectful bow you can possibly do. (Thank you China, for bringing this word into Japanese and thank you Japanese for bringing this into English.)”

The WK explanation makes it seems like the word went Japanese → English but it went from Chinese → English Kowtow - Wikipedia

Am I misunderstanding the WK explanation text, or is it wrong? Thanks!

Edit: emphasis