I don't think the Royal Marines' drummers bringing their drumsticks horizontally up to the face is unique to them, although they are the only once I've seen doing it while marching/playing. In videos, I've seen drummers in the British Army's Foot Guards do it as a preparatory position (not while marching), too. As well, I believe the Drums of the Fort Henry Guard (portraying 1867 British infantry at Old Fort Henry, Kingston, Ontario) also bring the drumsticks up to the face as a preparatory position prior to playing. My experience in 18th c. British Army reenacting revealed that some of the drummers in those recreated units raise their drumsticks horizontally to their face as a preparatory position. So it appears to have an historical precedence. Of note, the U.S. Merchant Marine Academy Band copies the Royal Marines in having drummers to the front and they raising the drumsticks horizontally while playing.