Longs are the opposite of shorts.
As to its usage - I am a native British English speaker born in the seventies and I've never heard it in 40+ years. The most common word would be trousers (or, in some regions you may hear the more informal word pants, but in other regions this word is reserved for underwear), and if needed we sometimes clarify that they need to be smart by saying smart trousers. It is generally accepted that "smart" dress excludes shorts.
However, while this word might be in a British English dictionary, I'm not sure your guide is written by someone speaking British English, or any good form of English, as the term "smart/casual" is written with a slash. This makes it look like an "either" option, yet the two are quite different. Surely they mean "smart casual"?
The term "smart casual" is widely misunderstood. What it actually is changes with time and fashion, but generally speaking it means a smart form of dress that is not formal like a mans suit or a woman's cocktail dress. For a man it means trousers (not jeans) with a shirt and shoes. But many think it means combining smart things, like a shirt, with something casual like jeans and trainers/sneakers. This is thought of by some to be a massive fashion mistake.
My point is, whenever you see "smart casual" on an invitation, for the reason given above it is not uncommon to see some kind of clarification such as "no jeans", or even specifying tuxedos or ball gowns / cocktail dresses for formal events. In your example, they are trying to say "no shorts" by specifying that long trousers are expected.