It is becoming evident to me that the author does not want to think out a reason why it would be rational for either the British alliance or the French to press on and force the other over the brink into all out war. I think it is plain that the deep balance of interests at the time tended to damp out global war or sustained war between Great Powers, the author's own evidence helps make that clear. There are times when the world is poised on the brink and a single spark can set it off, indeed arguably if we laboriously butterfly one spark (to set off the Great War of OTL) then that merely delays it until the next spark, because the tinder is dry and oiled and the bonfire is ready to go. Other times you can flail around with butterflies equipped with flamethrowers and the flames you start will be put out. The French know they aren't ready for war with Germany, there is no guarantee the Germans won't come in and knock them back more notches while they are distracted with fighting Britain. The British evidently don't want war with anybody except weak native peoples at this time (and the Boer Wars showed that it was wise of them to avoid fights at this time). The Germans, as the author said, don't want war with anybody right now; this leaves the Austro-Hungarians and the Russians and perhaps the Turks to start Some Damned Thing in the Balkans, but at this time we'd expect the Great Powers of the Concert of Europe to either sit back and watch, or sit on these eastern powers until they stop.
I think I would probably be borne out in these impressions by any careful student of the era.
However, I do have to admit that war can be pretty silly in its causes and is hard to stop once started. In Siam, as at Fashoda, even if fighting does get out of hand locally I'd expect both Paris and London to take steps to damp it down and end it. The author has not identified a fault line in history but merely one of many incidents which demonstrate, rather than the likelihood of war in this era, its very opposite. This is my impression. But perhaps people are just plain crazy and war can happen any time, with small shifts of mood, for any reason.
Anyway from the number of posts devoted to mustering battle fleets and orders of battle for armies on either side, it is evident the goal here is not to have a plausible AH but rather a war game, to try to game out what could have happened militarily if we all just stop worrying about political plausibility and go with the theory of history expressed in Red Dawn--"sooner or later the biggest two kids on the block are gonna fight!
It so often happens in TLs that I throw my hands up, typically when it a TL logically comes to a juncture where war is imminent, and say "this has to be gamed out by experts." I therefore hope there are some war gamer experts around who can plausibly explain how it would reasonably go down, who has the edge and who is going to lose, and why and how and where and when. I can't do that. I should be grateful there are people who can and who want to. And therefore, having determined that the author has no particular POD in mind beyond "the French and Siamese fight" where from where I'm sitting either one of them would be crazy to, and adds that the British get sucked into the vortex with all out war against France instead of just trying to put out the fire in Southeast Asia. That's it, then the dominoes start falling. I don't see any plausible reason why the French should not worry about Germany piling on, but then again, the Germans certainly could opt to stay out if they choose to, and the French will be grateful for the moment if they do stay out.
The author has set up the board of a war game and wants to play it out. If that is the case and that is clear, I say, fine, let that happen then.