When Britain entered the First World War, it had no formal sniper program. Germany was the first combatant to train and utilize snipers, and their effectiveness quickly convinced the British military that a similar program was necessary. Initially a wide variety of rifles were put into service, including many scoped hunting rifles send form the British Isles. These were of little use, as they were in non-standard calibers, and not generally rugged enough to survive the rigors of WW1. The first uniform equipment purchased and used were several versions of Galilean optical sights.
Introduced into competition shooting at Bisley before the war, this is a type of magnified sight which uses independent lenses mounted to the front and rear of a rifle (some fitted to the SMLE rear sight and some attached to the back of the receiver). This was low profile, relatively inexpensive, and quick to put into service, but the sights themselves were severely handicapped compared to modern telescopes. They offered about 2.5x magnification and a very large depth of field, but at the cost of a very narrow field of view and small eyebox. They were also easily dirtied, and the front aiming point was often difficult to discern against the background image.
The four main models purchased by the British were Lattey, Neill, Martin, and Gibbs. The model in this video is a Martin, patented by J.E. Martin of Glasgow. Once proper telescopes became available, they rendered the Galilean optics obsolete, and very few survived the war.