This was observed on Windows but may also affect other platforms.
If a DS4 is paired over Bluetooth and also connected with a micro-USB cable to the same computer, Chrome treats each connection as a separate device instead of recognizing it has two interfaces to the same device. This may also affect other devices that can support simultaneous Bluetooth and USB connection modes.
To fix this, Chrome should query the DS4 for its Bluetooth MAC address to identify the device and coalesce entries that have the same address.