The 1E DMG is full of what I consider to be really bad advices (among some good, some endearing, some inspirational and some just boring stuff), but "THE GAME AS A WHOLE FIRST, YOUR CAMPAIGN NEXT, AND YOUR PARTICIPANTS THEREAFTER" really takes the cake. Really, it sounds like he wants your own made-up world to take precedence over the fun and, quite frankly, the well-being of your fellow players, like our games are more important than them. I'm quite happy we collectively made some progress from there and that most games and players today recognize that the proper hierarchy is, the players (among which there might be a DM), then the game, then far and away the rules.
You do need to bear in mind the context, though. I don't think he's arguing against fun here at all. He's talking about aiming for long term campaign enjoyment, and for supporting the fun of other groups and DMs as well as your own. He's assuming multiple DMs in the local community, and that players and maybe characters will be moving to and from different DMs' tables/dungeons. This goes along with his advice on starting money & equipment on page 25, on time in the campaign on page 37-38, and placement of treasure and magic items on pages 91-93. Where, for example, he frequently advises not to be too generous, to keep the players hungry for more, which he believe maximizes how long the game remains exciting and satisfying.
With that in mind, more charitably, I would interpret those more like:
The game as a whole = Everyone's fun and future enjoyment, not just today's. This includes things like making consistent rulings, being fair, and not being either a "Monty Haul" or a "killer" DM, thus "spoiling" or traumatizing players who will then carry over unreasonably generous or harsh expectations both to future sessions and to other tables and players/DMs.
Your campaign next = The same, but at the smaller scale of just your ongoing campaign world and the games you run in it, which aren't expected to always be for the same players.
Your participants = the folks at your table for any given session.
I was able to infer a lot of this from a pretty young age, reading the DMG, but it's become increasingly clear over time as I learned more about the wargaming and RPG clubs where Gary and a lot of people were playing in the 70s and into the early 80s, at least. Reading Gary Alan Fine's sociological work
Shared Fantasy a few years ago vividly illustrated what a lot of players and groups were like, and contextualized Gary's advice.