Quick guide to spotting affiliate links and why not properly disclosing them can be a problem.

What is an affiliate link? - It is a link to a product and/or store which provides a monetary kickback for every product purchased using that link.

Which stores have affiliate programs? - Too many to name, but some of the most common and relevant when it comes to gaming are Amazon and G2A.

How do I spot an affiliate link? - Affiliate links usually contain extra information and are longer than regular links, because they contain a unique identifier which tracks where the click came from. This allows the retailer to pay the commission to the affiliate for any sales resulting from that click. Here is an example of an Amazon affiliate link compared to a regular link.
http://i.imgur.com/RjIG0Qu.png
G2A affiliate links usually begin with g2a.com/r/ followed by a username and are a little easier to spot. In both cases, anything you buy through that link, not just the specific product linked, can give a small percentage of the sale as commission to the affiliate.
Sometimes sites and Youtubers will use a link shortener, which can effectively obscure the affiliate link. This doesn't mean they're doing it on purpose, link shorteners are useful in general for many legitimate reasons. Some link shorteners let you see what is behind the link before you click it. An example of this is bit.ly. Add a + to the end of any bit.ly link in your address bar and it will show you a stats page and the full URL of where the link is going. This will help you determine whether or not there is an affiliate link behind it.

Why are undisclosed affiliate links a problem? - While affiliate programs are legitimate and above board in the vast majority of cases, the problem with not explicitly disclosing in clear view that the links in your video or article are affiliate links is that the viewer is not made aware that you have an incentive, however minor, to encourage them to buy the product, which could affect the content of your work. This can introduce an element of bias that the user must know of otherwise they cannot make an informed decision about the content of the article/video. Does this mean every article/video with an affiliate link is just shilling a product? Absolutely not, in fact the vast majority are not, but the risk is there and users should be told about it up front.

Isn't this just you telling other people what to do? - No, this is based on what both the FCC in the US and the ASA in the UK have said.
The FCC guidelines are very clear and have a specific section just for this subject. You can read it here under "What about affiliate or network marketing?" - https://www.ftc.gov/tips-advice/business-center/guidance/ftcs-endorsement-guides-what-people-are-asking
The ASA guidelines are a little harder to find but a couple of good explanations can be found here
http://www.brightdigitalminds.co.uk/clarification-ad-disclosure-affiliate-links/
and here http://blogtacular.com/sponsored-posts-ads-reviews-the-asa-and-your-blog/

Isn't it ok just to have a policy disclosure somewhere on the site? - No. Both ASA and FCC regulations clearly state this is not sufficient and the disclosure must be included alongside the links so users don't miss it and in clear, unambiguous language.
Conclusion - In most cases affiliate links are just fine and not a big deal, however I think its important we all try to make sure we are never potentially misleading our audiences. Sites and Youtubers (especially Youtubers lately) can do a better job at this and now the rules are crystal clear, there's no real excuse not to anymore.

Hopefully this was useful information.