JSFiddle seems to be using an older version of TypeScript. They are generating the following JS:
var Person;
(function (Person) {
Person[Person["firstName"] = "First Name"] = "firstName";
Person[Person["lastName"] = "Last Name"] = "lastName";
})(Person || (Person = {}));
document.querySelector("#app").innerHTML = Person["Last Name"];
The same code on TypeScript Playground generates the following with every version you can choose on there:
var Person;
(function (Person) {
Person["firstName"] = "First Name";
Person["lastName"] = "Last Name";
})(Person || (Person = {}));
document.querySelector("#app").innerHTML = Person["Last Name"];
This appears to be an open issue on their GitHub: https://github.com/jsfiddle/jsfiddle-issues/issues/1079. That thread states that they are using version 1.7.3.