Originally this request was for only impressions, no clicks. In order to track clicks this needs to be done in the page source in one of two ways:
1) Add an attribute to each link where you want to track clicks. This attribute is "manual_cm_sp" (site promotion) or "manual_cm_re" (real estate). This is Option 2 in the link you provided.
2) In the "href" attribute of the link you can add "cm_re" or "cm_sp" in the query string. it would look something like:
These values have to be on the page before the CM library loads. So it will need to be done by your developers or either of these methods can be done via Tealium using a JS Code extension to inject these values into the page. Also, both methods will also initial an impression automatically. So if you use either method you will need to replace your current impression tracking method as well.
Unfortunately this is a very proprietary way of tracking these clicks, which makes it really difficult to simplify via Tealium. I would reach out to your Account Manager who will be able to pull in a resource and advise on the best way of implementing this.