Need a little small engine assitance, if possible...

Yes that's all part of the vent. But if it falls apart the vent will still work; now it will just leak.
If you look at the top you will see a tiny pinhole in it, and that is the hole where air is supposed to enter the tank. In the lower pic you see the backside.The splined thingy is just the retainer system for anti I-lost-my-cap system. It matters not to the vent if it's there or not,however there is usually a little thin foam puck trapped by that retainer in the cavity above it. And that foam is kindof a one-way valve. It allows air in, and vapor pressure out, while not allowing liquid fuel to leak alll over during the course of operation and especially when you hang it up afterwards.
It may not be broken as much as just it has just come apart. Go look for the foam puck and just press it all back together.In lieu of a puck, I have seen a metal disc in there, sometimes concave/convex which may need to be oriented correctly.
Louie70 talks about a paper gasket with a hole in it. That's the same kindof deal; it allows air in and acts as a splash baffle to not allow liquid fuel out. but your cap appears to be a little more sophisticated,lol. The paper thing was used for many decades.