ECMAScript 5+
No, quotes were not needed since ECMAScript 5. Here's why:
As mentioned in your post, from the ECMAScript® 5.1 Language Specification:
7.6 Identifier Names and Identifiers
Identifier Names are tokens that are interpreted according to the grammar given in the “Identifiers” section of chapter 5 of the Unicode standard, with some small modifications. An Identifier is an IdentifierName that is not a ReservedWord (see 7.6.1).
[...]
Syntax
Identifier ::
IdentifierName but not ReservedWord
By specification, a ReservedWord is:
7.6.1 Reserved Words
A reserved word is an IdentifierName that cannot be used as an Identifier.
Syntax
ReservedWord ::
Keyword
FutureReservedWord
NullLiteral
BooleanLiteral
This includes keywords, future keywords, null, and boolean literals. The full list is as follows:
break do instanceof typeof
case else new var
catch finally return void
continue for switch while
debugger function this with
default if throw
delete in try
7.6.1.2 Future Reserved Words
class enum extends super
const export import
7.8.1 Null Literals
null
7.8.2 Boolean Literals
true
false
The above (Section 7.6) implies that IdentifierNames can be ReservedWords, and from the specification for object initializers:
11.1.5 Object Initialiser
[...]
Syntax
ObjectLiteral :
{ }
{ PropertyNameAndValueList }
{ PropertyNameAndValueList , }
Where PropertyName is, by specification:
PropertyName :
IdentifierName
StringLiteral
NumericLiteral
As you can see, a PropertyName may be an IdentifierName, thus allowing ReservedWords to be PropertyNames. That conclusively tells us that, by specification, it is allowed to have ReservedWords such as class and var as PropertyNames unquoted just like string literals or numeric literals.
ECMAScript <5
To go more in depth as to why this wasn't allowed in previous versions before ES5, you have to look at how PropertyName was defined. Per the ECMAScript® 3 Language Specification:
PropertyName :
Identifier
StringLiteral
NumericLiteral
As you can see, PropertyName was an Identifer - not an IdentifierName, thus leading to the inability for ReservedWords as PropertyNames.