I agree fully that games should be treated as games and not as anything else.
However, games often overtly try to be movies, or at least try to challenge movies at their own home turf by applying lessons and techniques from movies (or, indeed, literature -- especially JRPGs and other japanese narrative-driven games). Thereby making it all the more tempting to just point out that they're often amateurishly put together.
My general point was just what you said: That story-driven games need to convey good stories that would be considered as such not only by genre stalwarts such as us, but by people in general.
Of course, all stories are subjective experiences and as such, I'm prepared to accept a lot of different views on what constitutes a good story. I did, however, find that in the mentioned example a writer well versed in drama theory and the defining stories of other mediums should have been able to point out that the story was in fact an amateur effort on a number of basic levels.
But as you say, agreement on this is perhaps a pipe dream.
