You can use this pass in the ICE trains between Brussels and Germany. In Belgium, it is not valid in any other trains. So if your home is in Brussels or Liège, then you can indeed use it to travel between Brussels and Cologne.
It doesn't matter where you start your trip.
OR OR-much better BIG bargain: there will be a MONTHly ticket for just 9 € in all of DE during the monthes of jn/jl/au-for the calender month, valid in ALL transport, except those fast shiny ICE/IC. They call that Fernverkehr, whereas the rest is NahVerkehr. For long distance however those ICE are far better, faster and comfy.
You likely know that local tix from NMBS are not very expensive and there are also loads of discounts.
I have to rectify myself. The conditions of use say: "One Country Passes are not valid in the country of residence of the Pass holder”
That means that if you live in Belgium, you will need extra tickets from/to the border.