By Malathi Nayak and Deepa Seetharaman SAN FRANCISCO (Reuters) – Amazon.com Inc, a company known for its ruthless drive, is courting the free-wheeling coders and dreamers of the gaming industry with a lighter touch as it seeks to break into an arena now dominated by Apple and Google. The online retailer, infamous for undercutting rivals and pressuring suppliers, hopes that making nice with game developers will help it build a vibrant app platform on its new Fire TV and gain ground in an area where it severely lags the competition. For example, Amazon last year contacted London-based developer Ashraf Hegab out of the blue. In contrast to the sink-or-swim style of Apples and Googles app stores, Amazon promised to promote his game actively if he brought it to its platform, he said.