There's plenty of battles on there that didn't involve Britain at all, Otranto and the Piave immediately spring to mind. If you use the sidebar and view battles by theatre, you will see non-British battles are well covered. Ironically, the French seem to get the worst deal, seems to be relatively little about Verdun (it hasn't been 'broken up' like the Somme has) or the 1917 offensive?
As far as I could see, there isn't a single battle on that list fought by Serbian army against Austria-Hungary in 1914 and against combined German, Austrian and Bulgarian forces later in the war.
I don't know of a single site that adequately covers all the major WWI battles. The 3 major fronts (in order of importance) are Russia, France and Italy.