It looks like your iframe parameters are a little garbled; there’s a couple style attributes and an out of place double quote. My assumption is that Chrome is still able to figure out a way to display it and Firefox is not. I would also recommend not using attributes like “bgcolor” and “text” as these are not compatible in HTML5. Here is a suggested edit for the iframe and using inline CSS:
<header>
<title>GTurbo.Club - Home</title>
</header>
<body style="background-color: #333333; color: #CCCCCC;">
<div style="text-align: center;">
<h1 style="color: #9966FF;">Welcome to GTurbo.Club!</h1>
<h5 style="color: #FFFF33;">This website is run off of Paypal Donations</h5>
</div>
<div style="text-align: center; margin: 0 auto; color: #000000; border: 4px solid #9966FF; width: 740px; height: 500px; background-color: #CCCCCC;">
GTurbo's live stream:<br />
<iframe
src="https://player.twitch.tv/?channel=gturbo"
height="480"
width="720"
frameborder="0">
</iframe>
<div id="paypal-button-container"></div>
</div>
</body>