Some sites email your password to you: https://plaintextoffenders.com/
1) A site that emails you your password might not be storing it in plain text. They're similar but separate problems.
2) A site that sends you a login link could be just as bad as the sites listed here, if that login link doesn't expire (and you used a unique password). It's a more subtle way of having the same problem.
If it's a password generated by the site, then it's actually fine to email it. Although you likely don't want it too early in the email that it would show up in a phone notification or in a body summary in gmail.
You could also just have a horcrux for a couple sites and make them all distinct obviously.
How did you eventually find out their true motivation?
His idea to make me sign up without a password manager was illogical anyways. If I use a password manager on his site, it should be obvious I use a password manager for my video game account, so me halting my password manager usage for his site wouldn't help him get my video game account.
I also agree somewhat about obscurity. Notice that I haven't said what password manager I use, or where I store it. The fact that I use a password manager I don't consider sensitive though.
I don't think that reusing the same pepper (horcrux string) for all sites would be best practice.
Joking aside, I don't see the point of this. It guards against exactly one attack (your password manager somehow revealing all your passwords) which is unlikely, but not against a whole lot of other (slightly more generic malware, phishing, ...) whilst making logging in harder (there's now a manual process).
If you're willing to go such lengths, enable 2FA on more accounts (which the articles mentions, points for that) or get a physical token for your password manager.
Another weakness that doesn't require a keylogger, is the attacker might be able to find some stolen database of a website that stored passwords in plaintext, then deduce your horcrux from the difference between what was in your password manager and what was in the database. And if the site did hash passwords, the attacker can try cracking the horcrux. The 5-character example horcrux probably wouldn't be too hard. The article somewhat covers this by saying only use the horcrux on important sites. This is good, but it still has weaknesses because an important site can still get its database stolen, and some people also want to protect less important sites.
And if no password databases are available, the attacker can create a website and ask you to join it under the hope you'll reuse your horcrux on the attacker's site. I've actually had an attacker contact me personally (that is, actually chatting with me live) and ask me to sign up for his forum under the hope that I would reuse my valuable account's password on the forum.