I agree forcing web site registration etc to post feedback can be a issue. However, you need to give users options or multpal ways to post feedback. However, users will rarely give you feedback unless they get something in return. I recommended a website as one way because its not platform specific.
Viewing post in I think we should have a review system.
I think if you have to incentivise them to give feedback with anything but your presence of mind, you probably don't want their kind of feedback in the first place.
It sounds like you're trying to cater to people who just try games willy nilly without a care.
If you have a game worth looking at, an immediately available comment section is all you need.