Yes. Those are the symbols used on NATO maps for units of various sizes. However he's obviously been brought up (despite being a citizen of the Commonwealth, and therefore cultural heir to the greatest system of military organisation ever
) on the US system - the regiment symbol is correct, but || denotes a battalion (or US regiment), | a company and below that we have ... for a platoon (or armoured troop), .. for a fighting section and . for a fire team or a below-strength section (for example, a recon patrol of four men).
I'll find a diagram if I can.
EDIT: Got some!
Formations by size:
A section (
c 10 men commanded by a corporal, sergeant or occasionally a colour/staff sergeant) is made up of 2 fire teams commanded by lance-corporals. A platoon (cavalry troop) is made up of three sections commanded by a lieutenant (pronounced leff-tenant) and contains 32 men (3 sections + OC + 2Lt) or 3-4 tanks in which case it is called a troop. A company (or squadron in the cavalry) is made up of three rifle platoons plus a company HQ (the OC and his people to co-ordinate the unit in battle; think intelligence men and that sort), and a batallion is usually made up of 3 rifle companies plus a HQ company and a manoever support company. A battalion forms the core of a battlegroup, the smallest 'unit' that is deployed into a theatre (generally an infantry battalion, an armoured company, plus assets like REME, Signals and so on). In the cavalry, battalion and regiment are synonymous (regiments are 1 battalion) and a Royal Marine battalion is called a commando.
Multiple battalions form a regiment which has a common identity but is almost never deployed together and rarely share a role - for example, 1 RIFLES is a commando-trained light infantry battalion while 5 RIFLES are armoured infantry. The SAS is known as a regiment, but each constituent part (21, 22 and 23 SAS) are also called regiments. A regiment is often officially commanded by a very senior officer (the parachute regiment CinC is a general), and a battalion by a Lt-Colonel.
Battalions are grouped together along with auxiliary bits to form brigades (for example, 3 Commando Brigade is composed mostly of 3 RM battalions (or commandos), 1 infantry battalion (1 RIFLES), 1 Royal Artillery battery and a Squadron of royal engineers). These group into divisions commanded by major-generals. A division is the largest force that the modern British army will deploy in 'peacetime' and if all ground forces (british army, RAF regiment and RM included) were mustered together they could probably make 8 divisions.
Above that we have a corps which has two meanings, the first being as in 30 Corps which means 'a group of divisions making a bloody massive formation'. The UK used to keep one of these in Germany, designated 1 (BR) Corps, whose role it was to defend West Germany from a Soviet attack; the second being as in 'Royal Corps of Signal' or 'Army Air Corps'. A Field Army is made up of at least one corps with some extra units, probably divisions, added on, and will have responsiblity for the best part of a theatre. Army Groups, Regions and Theatres come above that in that order (a Theatre would have responsibility for all of Europe, a Region for Western Europe, and an Army Group for France).