The biggest thing is that there's no reason to invade the US homeland. The "Enemy" would use first strike nuclear armed missiles and not bother with boots on the ground.
But even if you allowed the basis of the movie, there's still a huge problem. The kind of rebellion shown only works if there's another, bigger country supporting the rebels.
General Washington didn't beat the British; the French Navy did. The French resistance didn't kick out the Nazis; the Allied invasion at Normandy did. The Viet Cong had plenty of aid coming in.
According to the movie, Europe was completely controlled by the USSR and China had been nuked. Guns and bullets are expensive, and those kids could have only stored away enough for a few weeks of hunting, not a decades long war.
I think in the game they implied the first drop was in Virginia, all the soldiers parachuted airborne... Oh and btw I'm not referring to take the whole country, not even in the game the Russians managed to do that.
Oh and there's also fighter jets and the whole satellite surveillance is down.
They'd have to hack military air control. And even then they'd have to jam the communications between AWACS and local air units. Having one system isn't going to cut it.
Edit to add, since you mentioned a first landing in Virginia, they'd run straight into anti air defenses that operate independently of NORAD. Every woodline would shortly have an Avenger system and the 82nd Airborne would collectively scream in joy as they begged, borrowed, and stole every bit of rifle ammo they could find. They wouldn't even need orders. Their entire special training is to act without orders because Airborne troops are frequently cut off.