For just a base level of investment, it has to show some evidence of polish. Must look and control decently so that it's not a pain to interact with. Any awkward interaction is a huge detractor for me.
Once it nails that I will give it a fair shake and it can engross me in a countless number of ways. I can't really make a rubric for that! Because some games may have 'bad' stories but do their job very well in moving the player along, in which case I'd consider it a good story. Sometimes mashing a button is bad gameplay, sometimes it feels absolutely right. Things get very messy when you try to compartmentalize game design. One thing always effects another, which is why that base level of polish is so important.
Once it nails that I will give it a fair shake and it can engross me in a countless number of ways. I can't really make a rubric for that! Because some games may have 'bad' stories but do their job very well in moving the player along, in which case I'd consider it a good story. Sometimes mashing a button is bad gameplay, sometimes it feels absolutely right. Things get very messy when you try to compartmentalize game design. One thing always effects another, which is why that base level of polish is so important.