TSA says the following, verbatim
You may transport unloaded firearms in a locked hard-sided container as checked baggage only. Declare the firearm and/or ammunition to the airline when checking your bag at the ticket counter. The container must completely secure the firearm from being accessed.
Locked cases that can be easily opened are not permitted. Be aware that the container the firearm was in when purchased may not adequately secure the firearm when it is transported in checked baggage.. Emphasis added
Do you think that plastic case is easily opened? Can you easily pry it open with a knife or screw driver?
Finding out at the airport that it is not acceptable is not the time.
I use something more substantial. I would recommend you do the same.
You can read about traveling with firearms and ammo here
Transporting Firearms and Ammunition | Transportation Security Administration
Specific airline information may be found here.
Flying with a Firearm?