AFAIK PCIe is not accessible from JavaScript in the browser at least. Maybe some options in Node.js if someone has ported something to run there, but from the browser I am unware of any efforts to support that as an official standard at least. Only WebUSB which is what the above github repo demonstrates where by you can take a TFLite model, convert to the TPU Edge format, and then run via browser to USB Coral device, and do inference on arbitrary images etc.
Also right now WebUSB as far as I am aware is only supported on Chrome (and browsers built upon that stack) and due to then nature of the Coral USB TPU will require you to push firmware to the device when inserted (only need to do once while USB is inserted, but would need to redo if you unplug or power off), to access the chip that does the processing as detailed in the Github which means the user will have to allow access to 2 USB devices via the standard WebUSB popups.
My gut instinct right now is that Node.js may be easier to communicate with the Coral device right now as I think I saw some libs for Node that replicate WebUSB too and support USB Reset etc too. This would probably work well on devices like Raspberry Pi etc which are the sorts of platforms that need this acceleration anyhow as most modern laptops etc will run very fast with standard TensorFlow.js inference via WebAssembly or WebGL in browser