What is the reward mechanism for eating spicy foods? I can eat pure sugar and pure fats and find it pleasurable thanks to the taste receptors; and salt to a lesser extent. But pure raw chilli products trigger irritation to the tongue, cheeks and nasal passages.

So it seems chillies do not "win over" taste receptors the way sugar, fat and salt do, but we do crave it.

What is the reward mechanism that makes spicy foods desirable?
Rozin (1996) provides an introduction to the psychology of food. 
Rozin and Schiller (1980) present a study on the acquisition of preferences for chili peppers.

In the abstract, they write:


  Interviews, observations, and measurements were carried out in both
  Mexico and the United States. Exposure to gradually increasing levels
  of chili in food seems to be a sufficient condition for preference
  development. Chili likers are not insensitive to the irritation that it
  produces. They come to like the same burning sensation that deters
  animals and humans that dislike chili; there is a clear hedonic shift.
  This could be produced by association with positive events, including
  enhancement of the taste of bland foods, postingestional effects, or
  social rewards. It is also possible that the initial negative response
  to chili pepper is essential for the eventual liking. Chili stimulates
  an innate sensory "'warning" system but is not harmful. The enjoyment
  of the irritation may result from the user's appreciation that the
  sensation and the body's defensive reaction to it are harmless. Eating
  of chili, riding on roller coasters, taking very hot baths, and many
  other human activities can be considered instances of thrill seeking
  or enjoyment of "'constrained risks.


The paper also present research for and against desensitisation processes, although they note that this still requires some general rewarding quality to chilis.


  Chili preference might be related to receptor desensitization.
  However, there would have to be positive features of chili that
  support a preference once the desensitization took place; otherwise,
  desensitization would lead to neutral responses. There is some reason
  to believe that desensitization to capsaicin could be a factor in
  human chili ingestion. High concentrations of capsaicin placed on the
  skin of humans or rats produce drops in sensitivity to subsequent
  applications of capsaicin that last for hours up to days after the
  initial treatment (Jancs6, 1960). Systemic injections of high levels
  of capsaicin into rats and guinea pigs produce months-long complete
  desensitization to the effects of capsaicin and other chemical
  irritants. Desensitized rats do not respond (as with paw wiping) to
  irritating solutions of capsaicin or ammonia placed in their eyes
  (Jancs6- Gfibor &amp; Szolcs~myi, 1969)


References


Rozin, P. (1996). Towards a psychology of food and eating: From motivation to module to model to marker, morality, meaning, and metaphor. Current Directions in Psychological Science, 5(1), 18-24.
Rozin, P., &amp; Schiller, D. (1980). The nature and acquisition of a preference for chili pepper by humans. Motivation and Emotion, 4(1), 77-101.