I'm trying to understand whether its redundant for me to include some kind of CRC or checksum in my communication protocol. Does the chrome.serial and other chrome hardware communication API's in general if anyone can speak to them (e.g. chrome.hid, chrome.bluetoothLowEnergy, ...)
Serial communications is simply a way of transmitting bits and its major reason for existence is that it's one bit at a time -- and can therefore work over just a single communications link, such as a simple telephone line. There's no built-in CRC or checksum or anything.
There are many systems that live on top of serial comms that attempt to deal with the fact that communications often takes place in a noisy environment. Back in the day of modems over telephone lines, you might have to deal with the fact that someone else in the house might pick up another extension on the phone line and inject a bunch of noise into your download. Thus, protocols like XMODEM were invented, wrappering serial comms in a more robust framework. (Then, when XMODEM proved unreliable, we went to YMODEM and ZMODEM.)
Depending on what you're talking to (for example, a device like an Arduino connnected to a USB serial port over a wire that's 25 cm long) you might find that putting the work into checksumming the data isn't worth the trouble, because the likelihood of interference is so low and the consequences are trivial. On the other hand, if you're talking to a controller for a laser weapon, you might want to make sure the command you send is the command that's received.
I don't know anything about the other systems you mention, but I'm old enough to have spent a lot of time doing serial comms back in the '80s (and now doing it again for devices using chrome.serial, go figure).