I had been through array destructuring syntax, which is well understood.
What exactly are we doing below, when we say var {p, q} = o;?
Is
That's because using your syntax for object destructing, the names used in the LHS expression ({a, b}) are used as keys into the RHS expression (o). Since a and b are not properties of o, that fails (returns undefined).
The relevant section in the spec for this is in Runtime Semantics: DestructingAssignmentEvaluation under AssignmentProperty : IdentifierReference Initializer (2nd from last). AssignmentProperty are your a (and b... separately), and. The StringValue of a is 'a' and that is used as a key to get a value from o (equivalent o['a'] in this case).
It would work if you'd do:
var {p:a, q:b} = o;
which uses AssignmentProperty : PropertyName : AssignmentElement (last entry) which uses a propery name (p) AND an assignment element (a).