Those who would give up Liberty to purchase a little Safety, deserve neither Liberty nor Safety.
They launched a (ballistic) missile which made a rather hard rendevous with the target. Almost the same procedure like when a freighter makes a flight to the ISS. Only that the freighter slows down before meeting with the ISS...
Why would the Chinese take out GPS? What system will their precision weapons use to hit their targets?
(They use GPS just like we do)
I think US armed forces are much more reliant on precision weapons and therefore GPS than Chinese. So shutting it down would certainly benefit them. But shooting "down" GPS satellites is still impossible; they are over 20000 km away, and this missile can't reach even 1000km.