In short: You can provide your own login credentials to read your fleets and stars e.g. https://nptriton.qry.me/game/5182163620986880/full?alias=qwerty&password=abc123.
Don't worry, the password travels securely over https. No 3rd party can steal it.
Long: To acquire the game data, I have created a dummy account that I use to authenticate with and then query the triton API.
The game and the API allows any visitor to read any game's public data.
<![CDATA[// a dummy account for public access to games
$auth_alias = "public_redacted_api";
$auth_pwd = "redacted";
// possibility to use user's account instead - needed to get fleets and stars data
if (isset($_GET['alias']) && isset($_GET['password'])) {
$auth_alias = $_GET['alias'];
$auth_pwd = $_GET['password'];
}]]>
This basically means, that you can use your own credentials for the api request, which will allow you to read any of your games as if you logged in yourself.
Just keep in mind that even though I am not doing anything malicious, I COULD STILL ACCESS YOUR PASSWORD! So just to be safe use unique password.