Translation:This is the highest mountain in the world.
"Der Welt" is in Genitive here, if I'm not mistaken. Yes, you don't need to put "in" here because the connection of "world" and "mountain" is made by using Genitive case.
In English there are no cases, so we have to use prepositions to connect the nouns. In other languages where there are cases, prepositions are not always necessary.