Observational Equivalence of open terms in PCF
Got the answer, thanks to jonsterling on reddit for the insight. 

The error is that both M and N written as full judgements, must be weakened to have the same environment, and one that fits C[-]. So the question becomes whether  ⟦M⟧ = ⟦x,y ⊢ x⟧ and ⟦N⟧ = ⟦x,y ⊢ y⟧ are observationally equivalent.  And the contradiction above disappears.