The billable answer is that many variables arise when choosing a domain name similar to an existing trademark. For example, you may be able to use your domain name if you can show that consumers aren't likely to be confused by the two names, or that you are the first (or "senior") user, or that you are not offering the same services. Say, for example, the other company offers gambling services and you offer "gaming" services (in which you assist in the removal of some species of Australian vegetation). Or, perhaps your site helps people with "gaming" the Medicaid system. If those arguments fail, there's always the possibility that you could challenge the trademark registration on the basis that it is "merely descriptive" (or the generic term) for what the service offers.
The fact is that even unrelated services -- say, wildlife preservation vs. pro wrestling -- can trigger problems. You'll also get hassled if you acquired the domain name primarily to profit by selling it to the other company. The Dear Rich staff would recommend you err on the side of caution, since gambling enterprises are usually well-funded and unafraid to litigate -- or, as our staffers put it: "the bigger the headache, the bigger the pill."
