To my knowledge,
Diagonal Dominance is actually a mathematic pattern, not a compositional guideline. In relation to photography, this may refer to the compositional guidelines of Convergent Lines, Convergent Diagonals, Dynamic Diagonals, Complimentary (or Parallel) Diagonals, Perspective, etc. I have not heard of any de-facto or official compositional rule or guideline called Diagonal Dominance, but diagonals are indeed a strong aspect of many compositions.
The best explanation of diagonals in composition, as well as composition in general, is probably found in the book "The Photographer's Eye", by Michael Freeman. This book is a superb work that clearly explains all aspects of photographic composition, and covers many topics of composition including diagonals, spirals, rules of division (thirds, golden ratio), etc.
In a general sense, diagonals can be used to great effect to guide the eye. Convergent diagonals can help you guide the viewers eye to the point of convergence, highlighting whatever may lie there. Zig-zags are similar in this respect, in that they are structured diagonals that guide a users eye "through" a photograph, rather than to a specific point of interest. Dynamic diagonals is based on the theory that diverging and/or parallel diagonals can add energy to a photograph. Perspective is another powerful yet subtle form of diagonals that can give photographs depth, as well as division and separation.