Is the China Card removed from the Early War deck before the initial shuffle in Twilight Struggle?
Yes, the china card is removed from the Early War cards before the shuffle.  You are right, it is harder to make a mistake with your explanation.  However I think that the rules are clear as they are.
As a side note, there is a computer implementation of the game that enforce the rules. Playing that version can help discover rules that you might have missed.
https://store.steampowered.com/app/406290/Twilight_Struggle/