The ID sync described in the doc you provided is a sync between AAM UUID (device ID) and Partner or Data provider ID.
There are two types of ID sync that can happen on the front end when a customer visits a website or an app:
1. Customer signs in with their customer id and sync happens between that CRM ID (Customer ID) and Audience Manager Device ID (AAM UUID). To implement this type of ID sync, you either define an ID sync code inside your DIL initialization code (also known as DIL custom code), or you can do that using Marketing Cloud ID service (Visitor ID service) using DTM or JS methods, as explained in these docs : https://helpx.adobe.com/audience-manager/kb/real-time-id-syncinaamusingdtm.html
So, overall this type of ID sync is for inbound traffic to your site or app.
MID (marketing cloud ID) can be obtained from AAM UUID and AAM UUID can be obtained from MID (if experience cloud visitor id service is implemented ) on AAM servers, since MID is generated from AAM UUID by some mathematical function.
2. Customer visits the website that has AAM implemented and the website owner has got a server to server destination for an Ad network or any DSP. Now, when a visitor comes to a site, AAM identifies it as it's own ID say 1234, and the ad platform will identify this customer with ID: ABCD. There needs a sync between both of these IDs. Here is a help doc on this type of ID sync : ID Synchronization for Outbound Data Transfers
If you are a data provider or a partner, and want to implement or change the type of outbound sync. Then, you will have to contact our Partner integrations team or visit Adobe Exchange forum : XC Partners