Newly registered domain, trying to set nameservers; am I missing something?

According to a WHOIS lookup, http://st.ki is not registered. DynDNS is not domain registrar for the .ki TLD, although you can certainly use the Custom DNS service with that domain. You will need to find a .ki registrar and register the domain name, then set the domain to use the Custom DNS nameservers:

ns1.mydyndns.org
http://ns2.mydyndns.org
http://ns3.mydyndns.org
http://ns4.mydyndns.org
http://ns5.mydyndns.org

Edit: Here is a list of TLD's we support domain registrations for. It is limited in number because most countries require registrars to have an actual physical presence in that country or have too many other restrictions to make it worth while: http://www.dyndns.com/services/domains/tlds.html

Custom DNS supports just about every TLD out there with a few minor exceptions: http://www.dyndns.com/services/dns/custom/supported-domains.html

Hm, my intention was to register the domain here, as DynDNS is listed as a registrar for the .ki TLD. However, after digging deeper in this site it looks like they aren't. I must have bought a CustomDNS package without a domain, despite all confirmation emails and zone options leading me to believe I was being productive!

Don't worry, if you can't get your .ki domain registered elsewhere, you can cancel your DynDNS Custom package within 30 days. See the refund policy.

DynDNS is listed as a registrar for the .ki TLD.

Oops, where is this? DynDNS support almost all domains for DNS hosting, but not so for domain registration. Could it be that this has been mixed up?

Edit:

Via Wikipedia's link to this website, they list the approved registrars for the .ki TLD: http://nic.ki/index.php/registrars.html

That's true. Too bad that DynDNS don't seem to know about it. ;-)
You may want to inform them about these news.

It doesn't look like you completed the registration process, or you didn't purchase a domain but some domain level service. I don't see any domain registration entry for st.ki. Are you sure you completed the checkout process with DynDNS? Do you see a domain registration entry in your account for st.ki?