Well, the gist of the story is about magic users called travelers. Travelers can open rifts into pocket dimensions. 11 dimensions are described in the books, but I am sure new ones could be developed. In these dimensions, the traveler can develop powers and meet spirits/avatars that they can use/summon into the "real" world. Each dimension has it's own unique limit to how often the traveler can call upon the powers of the dimension. If a traveler surpasses that limit, he transcends into an Incarnation of the dimension. Essentially a NPC.
In the house of chains, also referred to as Valinhall in the books, the limit is expressed by a tattoo of chains that appears on the character as he uses the powers of the house. As the chains progress, they eventually meet up and connect around the neck of the character. At that point, the character becomes an Incarnation and a NPC. The powers of the dimension focus on giving powers internal to the character, i.e. inhuman strength, speed, natural armor, rather than external powers like the other dimensions.
I can immediately see an application of the Hunger track for the limits on the house, but I am not as clear as to the summoning abilities in the game. I was hoping to hear from others who have read the books and are a little more familiar with the DFRPG mechanics.
The Traveler's Gate trilogy, btw, is written by Will Wight.