rxjs: TypeScript compile error: 'Promise' only refers to a type, but is being used as a value here.

I’m seeing the following compile error when trying to compile a small Angular/Rx project:

$ tsc -p .
node_modules/rxjs/Observable.d.ts(69,60): error TS2693: 'Promise' only refers to a type, but is being used as a value here.
node_modules/rxjs/operator/toPromise.d.ts(3,79): error TS2693: 'Promise' only refers to a type, but is being used as a value here.

RxJS version: 5.2.0

Code to reproduce:

typings.json

{
  "globalDependencies": {
    "es6-shim": "registry:dt/es6-shim#0.31.2+20160726072212"
  }
}

tsconfig.json

{
  "compilerOptions": {
    "outDir": "./dist/js/",
    "target": "es5",
    "noImplicitAny": false,
    "sourceMap": true,
    "module": "commonjs",
    "allowSyntheticDefaultImports": true
  },
  "include": [
    "./src/**/*",
    "./node_modules/typescript/lib/lib.es6.d.ts"
  ],
  "exclude": [
    "node_modules"
  ]
}

Angular service (edited)

import Rx from 'rxjs/Rx';
import {angular, ng} from "angular";

export class TweetEvents {
    requests = {
        getSentiment: new Rx.Subject<string>()
    }
    responses = {
        getSentimentSuccess: new Rx.Subject<Models.Sentiment>()
    }
    static $inject = [
        "$http"
    ];

    constructor(
        private $http: ng.IHttpService
    ) { 
        this.initGetSentiment();
    }

    private initGetSentiment(): void {
        this.requests.getSentiment
        .flatMap((search: string) => {
            return Rx.Observable.fromPromise(
                this.$http({
                    url: 'https://example.com'
                  })
            )
        })
        .subscribe((response) => {
            this.responses.getSentimentSuccess.next(response);
        });
    }
}

angular.module("events")
    .service("TweetEvents", TweetEvents);

I’m pretty stumped and can’t find examples online of other people with seeing exactly the same issue.