The only thing required to make betting like a market is for the gambler to be able to take the bookie's side as well. Many bookie's use Betfair to hedge their positions in fact.
In financial markets terms, a gambler is much like a prop trader. They're betting on a particular position. That position, unlike a more traditional financial instrument, will be the outcome of a race, game, etc. But this isn't really all that different to, say, betting on oil futures.
A bookie on the other hand operates much like a spread trader. They (try to) take a neutral position and just make money on the spread as the difference in the odds between taking and making a bet is really a bid-ask spread.