You make a good analogy there jess, but although the two situations are similar, there are some key differences in terms of rules and regulations I think.
First of all, in the stock market, I believe when significant persons (CEO, CFO, directors and other employees etc.) buy or sell shares in their own company, they are obliged to declare their transactions to the authorities, who in turn will notify the rest of the market. Their execution broker will be in breach of client confidentiality if they disclose any of the information related to the transactions privately to another third party. If the broker uses this information to trade in the company's shares before the information has been made public, then the broker will be committing an insider trading offence.
The main difference here is that trainers are allowed to place bets on their horses without the need for disclosure. Therefore, although the bookie in your scenario has breached client confidentiality by leaking the privileged information, I don't think it can exactly be classified as "insider trading".
Conflict of interests and corruption are also areas we can draw comparisons to.
Are JCA panel members allowed to place bets on races?