Unfortunately the lines are a bit fuzzy, but you shouldn't trip over any doing what you describe.
You don't say which country you are in, so the following applies to the USA. Other countries have similar laws but the details vary.
Writing or talking about how to play the game is entirely unrestricted; the words are your own and you can say whatever you like about a copyrighted work.
Screenshots count as derivative extracts of the original work; the exact shot you take isn't embedded in the game and isn't a part of the game, but graphics and design from the game will be included in it. You can use these under "fair use". This is where things get fuzzy. You are allowed to use extracts from a copyright work (like screenshots) provided you mostly meet the following four tests:
Your work is "transformative", meaning that, while it takes something from the original, it uses it to create something new with its own value. Your proposed course certainly does this, and this is the biggest factor in deciding fair use.
The nature of the work. You have more leeway when copying from factual works than when copying from fiction. A game would count as "fiction" for this purpose because it is not merely recounting facts (unless the game is an accurate simulation). You don't win any points here.
The amount taken. In this case you are taking aspects of the art-work and design for the game but you are not copying any of its functionality, which is the main value. This is another point in your favour.
The impact on the market for the original. People won't be able to use your work instead of buying the game, so the impact is very low. Another point in your favour.
So on balance it looks like you should be well in the clear. Unfortunately fair use is not something that can be decided with any certainty unless you get sued and a court actually rules on your case. Until then the most one can say is that, should a lawsuit ever happen, the court would very likely find in your favour.
I'm not sure exactly what you mean by "links", but if you mean links to URLs on the web then you have no problem: "deep links" which straightforwardly take the reader to another web site do not infringe copyright.