Only the first one is correct.
'across the room'
This means 'on the other side of' eg The bank is across the road, The USA is across the Atlantic
through the crowd of people
This is the same as 'He walked through the forest' . The crowd (like the trees) are a kind of obstacle that you have to penetrate through. This is different from eg 'He walked across the room' or 'He sailed across the lake', because in these situations there are no obstacles to make your way through.
I hope that's clear.