I sort of see "greatness" and "quality" the same way.
Now, I agree that you can measure certain things scientifically. Digital Foundry makes a living based on that.
But apart from frame rate and textures and lighting effects, can can you made a convincing case for objective video game quality? Some people like easy games; some prefer difficult ones. Online multiplayer is essential for many reviewers; for others its an afterthought. Complex menus and button inputs are off-putting for some, and immersive for others. Gameplay, by its definition, is a very personal, subjective thing -- it's how we as players interact with the rules of the game.
First off, that was a typo in my post there, meant subjective, but I think you got it.
And ya, I do absolutely think one can make a convincing case for the objective quality of a video, regardless of tastes. For starters, how are the production values? Visual design, sound design, etc. How do those match up to similar games, in the same genre? Does the game perform well on a technical level? Then, in terms of the gameplay, you're absolutely right that we all have (very) different ideas of what constitutes fun gameplay, but....does the game execute the intended gameplay well? Again, how does it stack up to similar gameplay in it's competitors? There are lots of very easy, objective ways to determine quality.