Transitvisa Beijing, what does third country or region means?

So, if your itinerary is:

Bangkok - Beijing - Amsterdam

Then you are definitely eligible for 144 hour visa free transit and you do not need any kind of visa. It is important to use correct terminology because this is not 144 hour transit visa, but 144 hour visa free transit, so there is no visa at all. Also, in Beijing it is 144 and not 72 hours because 144 hours has replaced 72 hours years ago.

Also, third country/regions means administrative unit that is different from mainland China...

As you can see, you are flying from Thailand (we can call it first country) then you land into mainland China (we can call if second country) and then depart to Netherlands (in this case, this is third country). To be eligible for this visa free transit scheme you have to have three different countries or regions within your itinerary. Beside countries, passengers can also use Chinese regions: Hong Kong, Taiwan and Macau. You have three countries in perfect order, so you are fine to travel visa free and to enjoy 144 hours in wider Beijing area.