Your site is probably vulnerable to this attack and there is very little you can do to prevent it. You can monitor for BGP hijacks but you can't really do anything about it when it happens.
The best you can probably do is pay for a TLS certificate signed by a CA that only signs certificate requests after actual, human verification, and pin that in a CAA record. This should prevent other certificate authorities from handing out a domain-validated TLS certificate.
If you're going for the monitoring route, keep the amount of domains your site connects to to a minimum. Self-host your fonts, frameworks, etc, so you only need to monitor your own host. If the developers of the attacked site had hosted their own JS, they might have noticed that something was up when the attack took place, because they can't know for sure if a route change for an external company like Kakao is intentional or a mistake.
The core of the problem is that advertisements by routers that have no business announcing specific routes like these are taken at face value. Certain ISPs that do not require RPKI or other security mechanisms will happily route traffic headed for your IP addresses to some router on the other side of the globe.
Web technologies like DANE used to be popular for this purpose (using DNS to distribute the certificate of your website, with DNSSEC validating the DNS records) but it has seen little actual implementation so far. HTTP key pinning (HPKP) was implemented in some browsers for a while, but its potential for holding websites hostage and general unfriendliness towards bigger websites caused it to be phased out.
If you have apps that operate your service, you can pin your TLS certificate in those and that should protect you against such hijacks.