JPR, that is not at all what the message implies.
App Owners DO NOT have the ability to steal your coins once deposited.
Furthermore, they DO NOT have any possession at all to coins that are deposited.
The warning has more to do with the fact that MoneyPot is not responsible for actions placed within the site itself. Moneypot can not control which actions are placed or verify that the site will do what they state they are going to do.
As for ownership of the funds themselves, they will always be on MoneyPot side. Even if the site disappears, you are still able to withdraw your coins back to Moneypot through their app page in MoneyPot.
Actually, I believe you are wrong there.
App owners can control* a player's balance in the app. As it clearly states Any money you deposit into the app gives it full control over that balance.
*tip or bet or whatever.
Edit: From FAQ.
What does it mean to deposit money into an app? What is my app balance?
To keep applications firewalled from your Moneypot wallet, Moneypot requires you to "deposit" bitcoin into an app before you can use/spend it at that app. If you have 1,000 bits deposited in an app, then the app only has access to those 1,000 bits. When you're done with an app, simply withdraw the app balance back into your Moneypot wallet. Alternatively, you can simply disable an app which will prevent that app from accessing the funds you're deposited in it. You can always re-enable the app in the future.
You only want to deposit money into apps that you trust. However, even if you trust an app's owners, you still want to minimize the amount of money you have deposited into apps. Imagine if an attacker breaches an app's database or finds an exploit that gives them access to your balance at that app. Or imagine if the app owner left their app's database password on a post-it-note near their computer and their roommate gained access to their server. Moneypot has no control over these scenarios, but you have control over the amount of bitcoin you risk at an app.
The point is that you need to remain vigilant about limiting the amount of risk you expose your money to. Since apps are created and managed by users, Moneypot cannot guarantee that apps are written securely. In other words, Moneypot does not know if an app has any security holes or not that, for example, would allow an attacker to spend your balance with that app. Moneypot does not know if an app owner has their database password sitting out on their desk.
Understanding these risks is crucial.