Chrome avoids it by installing into the User's own folder. Firefox is installed in Program Files, which requires user authorisation.
Arguably, this is the correct place to install, as it means that the application is usable by anyone on the PC, rather than having to be installed for each user individually.
Chrome does a non-standard install and also can be self modified which isn't secure. Chrome could be replaced by a keylogger+chrome by anything running on the system.
That's why admin privileges are required for accessing Program Files to begin with.
Using a separate updater process is actually the clean way to go, on Windows.