According to a recent report from the 2019 Game Developers Conference, various Nintendo Switch controllers will soon be compatible with Google Chrome via Bluetooth technology. Certain controllers, such as the Pro Controller, will also be able to be connected through a USB cable.
According to a denofgeek article:
This implementation replaces the experimental Switch Pro support on Linux, which is removed in this CL," the Gerrit page clarifies. The whole point of this update is to "improve support for Nintendo Switch gamepads" on Chrome, although no timeline was given as to when these updates will take effect.