Despite some (ab)uses - *.tv probably being the most notorious - two-letter Top Level Domains are assigned to specific countries. Some registrars are more permissive than others about what may be done within thier two-letter TLDs.
The rules in section 4 of that page reserve gTLD (generic Top Level Domain) equivalents within the *.io ccTLD (country code Top Level Domain) for actual residents residents of the British Indian Ocean Territory. Analagous to how *.com.uk generally indicates a business (com) in the United Kingdom (UK), they're saying that *.com.io must be a business in the British Indian Ocean Territory (and all the other gTLD equivalents).
In this context, a sub-domain is not by definition a third level domain. You can define whatever you want for sub-domains or hostnames within the domain they've allocated to your control. The host records you establish determine that.