const enums are one of the few cases where type information changes the emitted JS, something that's arguably a bigger problem than TypeScript-specific, but still just syntax sugar, syntax highlighted in the article.
Const enums are erased at compile time. If you have a reference to `MyEnum.VAR`, TS has to check whether the enum is a const enum, and if so, replace with something like `1 /* VAR */`. This means that the type information in one file (where the enum is defined) is necessary to determine the proper output of any file that uses it.