I've been looking at this personally. It's not stated in the article, but the initiative is known as constructive service credit for cyber direct commissions.
The way it works is basically the same as reserve officer recruiting, but with a higher starting rank.
You'd get in contact with an officer recruiter for the service branch you're interested in, using the normal channels. They have a deserved reputation for ghosting candidates, but they generally spend most of their effort on candidates further down the pipeline. One recommendation I got was to get in touch with an enlisted recruiter who can confirm your eligibility to serve and refer you as a qualified lead to an officer recruiter.
Air Force officer appointments are the most competitive (3-10% of people who meet all application requirements and medical qualifications are selected), and they are stingy on medical waivers.
The Navy is only slightly less competitive but reputed to be the most permissive with waivers.
One thing to know is that waivers for medical issues are issued without regard to your nonmedical qualifications. So if Jeff Bezos had a bad knee, that would disqualify even him.
