Yes, crusty old Objective C apps still exist. And they have to be maintained. It really isn't reasonable to expect developers to rewrite them in Swift just so they can use Amplify. I was recently asked to add Amplify to an app built in early 2015 before Swift existed. (Gosh -- are there really apps out there that are over 5 years old?!)

Fortunately, if you can bite the bullet and add Swift support to your Objective C project, it isn't so hard to make a Swift wrapper class that you use from Objective C. Here's one I created for free. It would be nice if the highly paid folks at Amazon would be kind enough to help us out with examples like this.

import Amplify
import AmplifyPlugins

@objc
class AmplifyWrapper: NSObject {
    override init() {
        super.init()
    }
    @objc
    public func initialize() {
        do {
            try Amplify.add(plugin: AWSCognitoAuthPlugin())
            try Amplify.add(plugin: AWSPinpointAnalyticsPlugin())
            try Amplify.configure()
            print("Amplify configured with Auth and Analytics plugins")
        } catch {
            print("Failed to initialize Amplify with \(error)")
        }
    }
    @objc
    public func recordEvent(name: String, category: String, accountId: String) {
        let properties: AnalyticsProperties = [ "category": category, "accountId": accountId]
        let event = BasicAnalyticsEvent(name: name, properties: properties)
        Amplify.Analytics.record(event: event)
    }
}

Use form Objective C like this:

#import "PutYourAppNameHere-Swift.h"

- (BOOL)application:(UIApplication *)application didFinishLaunchingWithOptions:(NSDictionary *)launchOptions
{
    [[[AmplifyWrapper alloc] init] initialize];
    ...
}

Then later on you can do this:

  [[[AmplifyWrapper alloc] init] recordEventWithName:@"App Opened" category:@"Counts" accountId:""];

Am I missing an installation step?

You're not missing anything. Unfortunately there's no Objective-C support on Amplify for iOS. Amplify was built in Swift using its full capabilities and Objective-C support is not currently being considered unless there's a strong demand from the community.

Out of curiosity: are you starting a new app in Objective-C? If so I would be curious to understand why not going with Swift given Apple's investment on Swift lately (Combine, SwiftUI, Swift language updates, etc).

If you're trying to integrate Amplify in an existing Objective-C app, then I'm afraid it won't be possible.