in die Welt:

Akkusativ: movement: into the world

in der Welt:

Dativ: state (here: movement within a place): inside the world

sind ... geworfen:

past participle of werfen: to throw. The participle here is used as an adjective, with passive meaning (Germans call this Zustandspassiv, confounding people...), like in "The window is broken" or in "I prefer broken windows".

werden ... herumgewürfelt

we are thrown around like dice. This is the German passive, formed with werden. In English you would not notice the difference, both sentences translate with are.
But you will notice the difference between into/ in die Welt and inside/ in der Welt. The first sentence makes an interesting presupposition:
if we are thrown into, there must be some outside, and a border between in and out. The second sentence only appeals to our direct experience.