Why do elderly adults benefit from sea water therapy for joint pain?

Not sure. History is full of accounts of "spa therapy" and in the 19th and 20th centuries and even today, many people believe in the healing powers of water therapy, particularly when that water is full of minerals. Athough I do not think anyone really knows how it may work, there are many people who feel better when they go into salt water. I would never discourage someone from doing it.
Sea water therapy. What therapy are you referring to. Perhaps hot sea water soaks would be effective due to bringing moist heat to the joints to relieve pain.
Some treatments... ...Work simply because people want them to work. The power of therapies with no obvious medicinal activity ("placebos") should not be underestimated. Water baths are also very relaxing, and reduction of stress will often result in reduction of pain.