The difference between these is actually not as hard as it seems, I think:
"would" indicates a hypothetical future thing:
I wish it would stop raining.
(If my wish were true, then it will stop raining some time in the (presumably near) future.)
I wish the game would be good.
(If my wish were true, then the game will become good, or will end up being good.)
In the context of the game, this might be said if, for example, somebody is releasing a new game but it hasn't come out yet, so you're waiting to see whether it will be good or not (but expressing this as a wish implies that you don't expect it actually will be good, or you're pretty sure it won't be).
On the other hand, past tenses are talking about a hypothetical past thing:
I wish it stopped raining.
I wish it had stopped raining.
(If my wish were true, then the rain would have already stopped at some point in the past.)
For example, "I wish it had stopped raining yesterday, but it didn't, so I was stuck inside all day."
Note that you can use the simple past for this, but it is actually more common to use the past perfect ("had stopped") instead.
Now, the use of "were" in your last example, is actually talking about a hypothetical present thing:
I wish this game were good.
(If my wish were true, then this game would be good right now.)
So, in summary, when expressing something hypothetical, like a wish, you are expressing your desire that:
- "would" -- something will happen in the future
- past tenses -- something did happen in the past
- "were" -- something is true right now