You have a number of options and which one you take will depend on your roommate's personality and reasons for cheating.
1) Directly call him out on it. Do it in a fun and joking way:
Hey roommate, are you cheating with your laptop there? We wouldn't approve of that round here (note that your tone should be light when you say this). He will hopefully close his laptop and laugh along, knowing he's been rumbled but it's no big deal. DO NOT do this if your roommate is likely to react badly to a bit of light teasing or if it's going to cause some long term bullying in your group.
2) Mention your discovery of the website lightly in a conversation (not in front of Jeopardy):
You know, I found this website that would totally make us all completely brilliant at Jeopardy.You could follow up with
Should we use it? That would totally be cheating. This will help you gauge how he views his cheating. He might simply be taking it less competitively and not see gaming the system as a problem. If this is the case, you could express your own opinion on cheating and make it clear that using this website is simply not on.
3) "Hack" the router. I assume your roommate is using WiFi (and I also assume your television isn't). Simply remove that option somehow. You can frame it as a group "challenge":
Let's see how we all do without the internet! or you can do it covertly. Unplug the router during Jeopardy. Access the parental controls/firewall and ban that specific site. This is more than a bit passive aggressive, and not really an interpersonal answer, however your roommate can never admit that his amazing answer site has now disappeared. If he was genuinely cheating (and not just gaming the system in a way he thought was funny), then he will be forced to stop and never admit to it.
4) Implement some "house rules". Similar to option 3, but much more overt. On a Monday, say, no devices during Jeopardy (just think with our own brains). On a Tuesday, maximise your score in any way (all devices allowed, everyone can cheat, fastest Googler wins). Your roommate can still play on the days when he's allowed a device, but you've effectively called him out on cheating and let him carry on if he wants to. There's no need to tease him if he only wants to play when he can use his device.