In all honesty I think the best thing you could do to support your ds is get away from assessing him as gifted/bright.
You've provided one source with a list that apparently defines the difference, but really-that's one list, other people will have totally different lists. I can think of a number of 4yos who would tick all except probably not performing above on the test, simply because they haven't been tested yet.
One I'm thinking of particularly is an absolute gorgeous little girl. Asked wonderful questions. What time zone is on the moon? She asked once. I love that idea. Her IQ was tested for a different reason. You see the question was whether she would cope in mainstream as she has learning difficulties due to a chromosome deletion.
I think it's the Doctor in the House books where he reads the Medical dictionary and concludes he has everything except Housemaid's knee. In exactly the same way if you have a list you will be finding you tick them all because the power of suggestion is huge.
The most gifted person I have ever known (2 Oxbridge degrees in totally unrelated subjects, one maths based, one essay based, done in 9 terms, finished by the time they were 19yo, got top firsts in both, in fact their maths' paper could have divided it in 2 and would still have got top firsts, and English was their third language.) the thing that struck you with them was how normal they were. You'd never have picked them out in a conversation or by what they were doing.
So forget about diagnosing him as gifted or even bright. Answer his questions, give him opportunities to learn things he's interested in. But also support him in the areas he's not so good at. Don't make excuses for bad behaviour and don't expect him to be constantly better academically than other children.
He will be much happier because you're allowing him to be himself, rather than boxing him in with a label that may weigh him down.