There are two separate problems:

1. Apparently, after the import, you never use playerModal.
2. There's no point to exporting the result of calling the IIFE, as it doesn't return anything; your const playerModal will be undefined.

I suspect what you're trying to do is import a module just for its side-effects. If so, you'd do it like this:

The module:

// No need for a function wrapper, modules run in their own scope
let modal = document.querySelector('.modal');
let startBtn = document.querySelector('#startBtn');

window.onload = function () {
    modal.style.display = 'block';
};

startBtn.onclick = function () {
    modal.style.display = 'none';
};

window.onclick = function (e) {
    if (e.target == modal) {
        modal.style.display = 'none';
    }
};

export {}; // You may or may not need this empty export, depending on your environment

app.js:

import "./DOM/layout/playerInput";

That just says "Import the module," without importing anything from it, which is how you load a module purely for side-effects.

That said, often having a module that you load purely for side-effects isn't best practice. You might instead have it export a function that you can call with the selector strings for the modal and startBtn that sets up the handlers (and returns a function to remove them).

The module:

export function setupPlayerModal(modalSelector, buttonSelector) {
    let modal = document.querySelector(modalSelector);
    let startBtn = document.querySelector(buttonSelector);

    const windowLoad = () => {
        modal.style.display = 'block';
    };
    const buttonClick = () => {
        modal.style.display = 'none';
    };
    const windowClick = (e) => {
        if (e.target == modal) {
            modal.style.display = 'none';
        }
    };

    window.addEventListener("load", windowLoad);
    startBtn.addEventListener("click", buttonClick);
    window.addEventListener("click", windowClick);

    return () => {
        window.removeEventListener("load", windowLoad);
        startBtn.removeEventListener("click", buttonClick);
        window.removeEventListener("click", windowClick);
    };
}

app.js:

import { setupPlayerModal } from "./DOM/layout/playerInput";

const cleanupPlayerModal = setupPlayerModal('.modal', '#startBtn');
// ...and then call `cleanupPlayerModal` if/when appropriate...

Or if there's really no need to remove those handlers:

import { setupPlayerModal } from "./DOM/layout/playerInput";

setupPlayerModal('.modal', '#startBtn');