Naval ranks relate to duties aboard a ship. The entire time I was in the Marine Corps, I served in the infantry. I didn't learn a thing about or even go near a ship. Some Marines do deploy on ships, but we just learned infantry tactics and deployed to Iraq and Afghanistan. It would have been strange to call each other seamen. Just a way of distinguishing ourselves based on what was expected of us, I suppose.

The Marine Corps lost touch with their naval roots during recent years, as America's wars have become increasingly focused on small unit tactics. The days of huge amphibious assaults are over, and the Corps is struggling to remain relevant.

Edit: I found a helpful link that states "In establishing the Continental Marines... emphasis on ships' detachments meant that the proposed battalions would be broken up into small groups; and this in turn meant that the organizations would have a comparatively simple enlisted rank structure."

Historically, "marine troops" were often just army infantrymen temporarily assigned to fight aboard ship. The Tudor warship Mary Rose, for example had a large complement of soldiers embarked when it sortied into battle. Although the British military had dedicated Royal Marines by the 1700s, army infantry battalions occasionally did shipboard fighting duty. And marine troops from every nation did a great deal of their fighting on land. There were Royal Marines at Lexington and Bunker Hill in 1775 and Royal Marines frequently landed ashore to make assaults during the Napoleonic Wars.

So using army-style ranks made more sense given the heritage and tactical role of marine units. So, when the time came to create the USMC, its founders likely just borrowed the practices of the Royal Marines.