Suppose a store sells vacuum cleaners of brands X, and Y. Suppose a salesperson receives money from company X whenever he sells a brand X vacuum cleaner. Suppose that X can clean pet hair, but that Y can clean pet hair much better than X.
You walk into the store and ask "We have a dog that sheds a lot of hair. What's the best vacuum cleaner for us?"
The salesperson has a conflict of interest. He has an interest in you being happy with your purchase and coming back to buy more things from the store. Selling you brand Y would serve that interest. But he will get money from the manufacturer for selling you brand X. Selling you brand X will serve his own self interest. These interests conflict with each other.
The writer hints that the Michelin guide put the Resorts World Sentosa restaurants in their guide and gave them better reviews than they deserved, because they are in a business partnership with Resorts World Sentosa.