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.
What if you find the soundtrack grating, and I find it mesmerizing? What if the realistic art style works wonders for you, and leaves me cold? What if I don't mind settling for 30 FPS and for you it's 60 FPS or bust? Which one of us is right? There's a big difference between the objective "this soundtrack was composed by Mr. X and played with A,B, and C instruments" and "this soundtrack is pure poetry and elevates the game from a rental to a must-buy." Surely you see the difference between a cold, objective presentation of facts and a deeply personal, emotional analysis?
You suggest measuring quality gameplay by stacking it up to similar gameplay in competing games? Well, to get there you'd have to assume some objective, quantifiable baseline, when, again, it's just your personal preferences, this time spread across multiple games.