Congrats on your new MCX!! And, welcome to the world of AR platformed rifles too! Your MCX pistol is an AR variant with some open source AR components, and many that are proprietary SIG parts. The muzzle taper is a good example of SIG's unique muzzle design.
The small steel ring in your box is a barrel Taper Cap. Taper cap is used if you mount a muzzle devise that isn't designed to fit the MCX barrel's taper just behind the muzzle threads.
When you have some time (this is a 51 minute video), here's a good MCX review you may enjoy
https://youtu.be/nXSaqafYeMQ
Here's a quick 1 minute animation of an AR's Direct Impingement or DI system vs the Piston system your MCX has:
https://youtu.be/K0QybgVsZSM
And, here's a video on improved cam pin parts to mitigate upper receiver wear many have had with SIG's new gen2 Carriage Assembly. A bunch of us are now running POF's Roller Cam Pin...
https://youtu.be/llOnufQ1zrY
Cheers