Now I know that website questions are a difficult thing to handle but in general I think it's better to leave them open. Now let me explain why:
First off let me list some of the biggest pros and cons of these questions.
The three biggest problems (and why they aren't that bad)
Actually I think the only thing we should worry about when it comes to the bad part of these questions is the third point.
Link Only Problem
The link only answer problem is true but let's be honest... There are a lot of questions with answers that are "too short" and a link-only answer just is basically the same as a "Yes or No" answer (and we don't close these questions, we just delete the bad answers). In the end a good answer always tries to explain the why, no matter if it's a Yes/No, a How do I do this or a Link Question.
Opinion based answers
Now this sounds a bit more difficult at first but I also don't see a problem too big to handle in this. The only thing that could happen here is that discussions about which website is better start. Everyone who answers the question can explain why they recommend this specific website. And yes the evil word "Recommend" has been spoken but it's not a real recommendation, since the asker should ask what he is looking for and unlike "I need a new Fantasy game like skyrim" websites about gaming information aren't a matter of personal taste. You could only find it more structured or maybe you like the design more (as long as the website is about the information the asker is looking for). Also if you get multiple answers it isn't necessarily a bad thing since you can expect multiple websites that serve the same purpose.
Poor research effort
As I've already mentioned this is the only thing that really is a big problem. You can find most websites with easy google search parameters like "Skyrim Mods" (Nexusmods), "WoW DPS results" (Simcraft) or "LoL Guides" (Mobafire). But I really feel like "Poor research effort" gets ignored far too often. I've seen a ton of questions with a lot of upvotes where if you google it the result shows up multiple times (yes most of the time also before that question was asked). Now of course when I see a question like "Where can I find League of Legends guides" I will downvote it because seriously... It's not that hard to type "LoL guides" into google. But a question like this can be specified. You could say for example "Where can I find lol guides for gold elo?" and if the asker asks tells in the question that he tried some of the websites google showed him but they don't work out, well then we have the potential to get a new maybe unknown website.
Finally I'd say those questions are still a grey area in terms of "can be asked" or "mustn't be asked". They have the potential to be good but they also bring some risks (but then again which question doesn't). Anyways I think those shouldn't be Closed. Downvote? Well maybe. If the question really Is bad dowvote it as hard as you can but don't close it. The answer to this question can still be an excellent one.
Now those examples were about website recommendations but what about the "How trustworthy is website X"?
As Grace Note already mentioned these questions are mainly for lawyers and we aren't lawyers. We are gamers. But one thing to keep in mind is that Gamer != Gamer. There are different kinds of gamers. There are the ones that just play games casually, there are the ones that Experiment with mods, the Professional players who earn their money with gaming and then there are also the researchers and Theorycrafters. Personally I'm a guy who is really into research and theorycrafting and I'm not the only one out there. So what I'm basically trying to say is: If you are someone who just plays a game and you learn things by playing that's totally fine but that doesn't mean a question about a website can't be answered! On SE it's "Experts answer your questions" and we are experts. But no expert can know everything. If you see a question about the validity of content of a Simulation or Statistics website don't just downvote and VTC it. Maybe you don't spend hours researching and calculating stuff in a game (which is totally fine) but there are actually people who'd rather calculate and search for information than play to learn a game.
Another thing to keep in mind is that questions about gaming software (even if it isn't the game itself) are allowed. And gaming websites should be considered as "gaming software". I know, I know... it's not an application itself but it's a website thats only purpose is providing information to one or multiple games.
- Should be upvoted and answered detailed if they show research effort
- Should be downvoted but not always closed if they show no research effort
Questions about website Content
- Should be Closed and deleted if the question is about legal issues or has nothing to do with the content of the game itself
- Should be left open if it's about the content of the website in relation to the game
Most questions about websites can be good questions and almost all of them can lead to good answers so don't just close them mindlessly.