It's a unary operator, kind of like ~ or !, which can apply to parenthesis (), until it meets a type, then the parenthesis are mandatory:

    int x;
    sizeof x;     // okay
    sizeof (x);   // okay
    sizeof int;   // not okay
    sizeof (int); // okay

It's a weird double rule to parse, but even worse, the strongest binding precedence typically doesn't like an alpha identifier at that point in the recursive descent, so you get weird rules like:

    read_prefix():
        is peak() '!': ...
        is peak() '~": ...
        is alpha(peak())
            maybe alpha is sizeof?
                wait, it wasn't sizeof? it was an identifier? long rewind
        is peak() '+': ...

Something like @ would've been a good pick for sizeof.

\ramble on

(actually, better yet, it should've been used instead of & for taking the address). Imagine:

    int x;
    int* p = @x;

\ramble off