The old Hong Kong ILS was actually called "IGS" (G = Guidance). The general criteria for runway-alignment is found in Pans Ops, for the countries using that criteria, or TERPS for the USA and a few other countries.
If the airport doesn't handle international flights, the regulator can establish any appropriate local criteria in consultation with the companies using that airport. The issue is a bit more complex for airports that handle international air traffic, but you could do worse than reading up on the simple few paragraphs in Pans Ops, that explain what constitutes a runway alignment.
There are cases, for example where the final segment only needs to cross the extended centreline of the runway, to be termed runway-aligned.