The Scala.js compiler, thanks to its static types, precisely knows which property accesses refer to "internal" properties (defined in Scala code, which can be renamed) and which ones refer to external JavaScript code (which cannot). It then simply always emit the former using dot notation (foo.bar) and the latter with bracket notation (foo["bar"]). This allows Closure to rename all internal property accesses but not external property accesses.
It's even slightly more powerful than using externs: if you use the same property name both in internal accesses and external ones, Scala.js can rename the former without touching the latter. An externs-based solution won't be allowed to rename the internal accesses.