• I tried using the @types/react package and had problems.
• I tried using the latest stable version of tsc. https://www.npmjs.com/package/typescript

I think you should consider to update these lines of code in order to support react 16 fragments

render(): JSX.Element | null | false | string | JSX.Element[]; //class Component<P, S>
interface ElementClass extends React.Component<any> {
    render(): Element | null | false | string | Element[];
}

https://reactjs.org/blog/2017/09/26/react-v16.0.html