I don't believe that Altium has a specific feature to construct antennas in a similar way that the software that you mentioned does, at least by default (I don't know if there is some extra plugin to do that available, I have never seen one). You can do your PCB antenna in the same way that you do any footprint for a component. In this specific case, you can do the following:
1. create a new footprint
2. draw the tracks on the top layer as the documentation describes and then copy the same tracks to the top solder layer.
3. Put an SMD pad on the tip of the track that you just drew and that is all.
Is that the answer that you are looking for? Let me know.