Hmm. I still play a mix of ADD 1E and Basic/Expert twice a week, and regularly re-read the 1E DMG. I think Gary has a lot of ideas about how D&D is best played, and is happy to share them, but between what's written in the DMG, all of his posts on dragonsfoot over the years, etc., I can't agree that he thinks the only way to play D&D (or even AD&D specifically) is the way he envisions it.

In fact, he's always known that the overwhelming majority of players have not ever played D&D the way that he did during the OD&D/AD&D 1e days. You have to remember that Gygax and Arneson's campaigns were much more like a tabletop precursor to MMOs than what we think of today when we talk about TTRPG campaigns. Both of them were running persistent worlds where 30-50 players were dropping in and out constantly, often with multiple characters involved in different things, multiple parties, etc. Time ingame ran linearly with time in the real world (thus Gygax's repeated insistence that strict time records must be kept), things happened in-world even when no one was playing, etc. But it's always been a tiny minority of games that were run this way, and Gygax knew it and knew that most people playing would have difficulty doing it the way he did.

You also have to remember that Gygax explicitly states in the DMG that players should not know all the rules and that you should distrust any player that has a copy of the DMG, and has many places where he recommends the DM adjust things as they see fit for their situation and table. He also was in favor of DMs fudging rolls when they believed it to be the right thing to do! And there's also his quote of “The secret we should never let the gamemasters know is that they don't need any rules” - to me, all evidence points towards Gygax believing that the heart of the game really was at the table.

IIR by the time AD&D 1st Edition Dungeon Master's Guide was published, there were already a bunch of blooming competing systems, with different dynamics between explicit and implicit, not to mention the combat systems. Those alternates include the Arduin Grimoires for example! Not everyone read or stuck with AD&D 1st Edition Dungeon Master's Guide but some did.

There was to me (it seemed at the time, given I was in middle school) a huge time gap between the AD&D Player's Handbook being released (April 1978) and when the DMG finally shipped (August 1979).

Dragon Magazine #22 (February 1979) eventually came out with a sneak peek at some of the tables needed to resolve combat.

Otherwise, yes, during that gap time there was a lot of homebrew solutions. Cobbling together elements from OD&D, Basic Edition (July 1977), 3rd party supplements (Arduin Grimoire, Jan 1977), etc. You did what you could with content gaps and often-conflicting sources.