Gary Gygax answered this question in an EN World interview, and at more length in Slayer's Guide to Dragons.

Originally there were the five chromatic and evil dragons, each with a color that suited their breath weapon, and a sixth good dragon patterned on the Oriental model of that imaginary creature. As it was both or different origination and alignment I decided to empower the gold dragon so as to more closely resemble the potent Oriental sort. So it got more of everything, including two breath weapons.

There came a time thereafter when more metallic dragons were desirable so as to expand the roster of good, Oriental-type ones. Thus all of them were modeled on the gold dragon template, had two breath weapons.

Logically, with metal value being used as the basis for potency, platunum (Bahamut) being the highest, then gold and silver, the sequence should have been platinum-gold-electrum-silver-copper-bronze. However, I thought bronze looked more potent than copper, and skipped then to brass—that metal conveying some not-so-benign connotations.

See http://rpg.crg4.com/originsD.html#dragon for the longer quote.

Tomb of Horrors appears to be the odd one out in terms of published adventures, originally designed very specifically as a challenge to his own group.

Gary Gygax himself said "There were several very expert players in my campaign, and this was meant as yet another challenge to their skill—and the persistence of their theretofore-invincible characters" The cover of the original ToH also states it was designed for tournament play, which indicates a far more competitive requirement than a normal adventure module.

I'd very much suggest comparing ToH to the style of, say, Temple of Elemental Evil which has much more of a balance with narrative and roleplay aspects when you read through it.

One thing to bear in mind is that his "style" was likely that of any good DM - to constantly adapt his style to fit the situation at hand. Given players that defeated everything he placed in their way with relative ease, he ramped up the difficulty. That doesn't mean he'd necessarily throw that level of difficulty at a different group. Any good adventure should be designed with a specific aim in mind, and a good author will tailor their work to that aim, rather than their personal gaming style.

This kind of approach can be seen in passages from the AD&D 1E Dungeon Master's Guide, such as "The testing grounds for novice adventurers must be kept to a difficulty factor which encourages rather than discourages players", and "If things are too easy, then there is no challenge, and boredom sets in after one or two games" - to me, that pretty much reads as "be a tough DM when your group needs one" and it seems he felt his group needed one. On the RP side, he clearly states "Place regular people, some 'different' and unusual types, and a few non-player characters (NPCs) in the various dwellings and places of business. Note vital information particular to each" and "When they arrive, you will be ready to take on the persona of the settlement as a whole, as well as that of each individual therein" so I'm pretty certain he didn't feel RP was something to be ignored.

Any quotes from players in his games should be taken with a pinch of salt, as they're undoubtedly going to apply to how he played with that particular group.

tl;dr: His style appears to have been to present the game that would best entertain and engage his players, rather than to play the game "his way".