The fact that Russia was so backward if probably one of the reasons why the Schlieffen plan seemed to be, and probably was, the most effectual. Had the German advance not been stopped at the First Battle of the Marne, it is likely that the war would have ended swiftly against the French (a far greater threat than Russia).
Attacking the Russians in full would have risked leaving the Western Front weak and the Italian Front not as well manned as it should be. In all honesty, the Schlieffen plan was the best option they had, and it was stopped by the fortunes of war.
In addition, your description from Darkest Hour fails to mention where the Russians/French declare war on you and why, and appears to lack an Italian front, but does mention that the British didn't get involved due to your remaining outside of Belgium. Historically, the Germans declared war on both the Russians and the French (out of fear that the latter would mobilize and surround Germany), so I'm genuinely curious as to why they declared war on you in that game as the aggressors. Especially considering the matter that in reality, Austria-Hungary initiated the war.
It's difficult to describe the beginning diplomacy, but on second thought i'm pretty sure i declared war on France after they refused to stay neutral. My bad.
But, as you said yourself, France was infact the stronger opponent, so wouldn't it make more sense to defeat the weaker one before facing the stronger one? Furthermore, remember that the borders between Germany and France were very well defended with trench networks and fortresses that had been in preparation for 40 years, infantry assaults would always fail, as that war showed us. I did mention the Italian front, the Italians declared war in mid 1915 and did some attacks on Trento along with a couple French corps, but after battles where they kept losing 150 000 men, they eventually stopped doing it. Remember that my plan was based around defeating Serbia very quickly, because i knew that Serbia was actually a though nut to crack, and how it turned out for the Austrians in the actual war. So unlike in WW1, i was able to redeploy the Serbian front to the Italian one, since the latter ended once the former begun.
I do agree that, in the German's point of view and why they chose the Schlieffen plan, did look like a sound plan with not many flaws. It's biggest flaw however was it's time table, if something went wrong there, many things would completely screw up. However the advance, of course, was halted literally by a miracle, the battle of the Marne.
I still think though, that keeping the British + Commonwealth out of the war outweights most of the advantages of the Schlieffen plan. Of course this is all in hindsight, and the German Chiefs of Staff probably knew a whole lot more than me, i still think defeating Russia first is a more solid plan.