Royal Marines connected shipboard policing with amphibious force

Did other navies use marines for extra-territorial and landing duties in the same way as the Royal Navy?

Not usually; the Royal Marines unusually combined routine shipboard landing-party duties with the ability to form a larger amphibious force.

Royal Marines aboard cruisers formed the nucleus of boarding and landing parties used during presence and policing missions. That shipboard function differed from navies that kept their marine infantry concentrated ashore until a larger deployment. During the Second World War the corps also developed a brigade-scale role, supported by attached army engineers and logisticians. The force could move between small independent landings and larger amphibious operations.