The point of the disclaimer is to restrict the claim to only the specific combination of words being asserted as a trademark.
One reason for doing so is to reduce the chance of the trademark being found overly broad or generic. Generic or descriptive terms generally can't be claimed as trademarks, and an attempt to own such a term might be grounds for refusing registration. To that end, the USPTO may require that an applicant specifically disclaim ownership of individual parts that can't be registered.
The result for you:
You can use the individual word being disclaimed, in any industry you like, as long as it isn't part of the phrase being claimed (but will probably be unable to register it as a trademark; there are probably reasons the other guy disclaimed it).
You can acquire a domain name consisting of the word. You might even get to keep it. Registrars aren't government entities, though, and aren't necessarily restricted to using US trademark law in making their decision.
Stay away from the actual trademark, though, especially if it's arbitrary enough to be distinctive, and double-especially in any industry even tangential to the other company's.