When his Time Machine gets stolen, the time-traveler that runs away from responsibility must stop his mad-with-power best friend from ruling time and space, and save the world.

A time-traveler, who uses the Time Machine to evade responsibility, must take the Time Machine back from a power-mad friend who uses it to rule time and space,

That fact that the thief is his best friend may be important for the turns, but is it really important now?

Good points above about shortening the descriptions. Possible rewrite:

When a irresponsible time-traveller discovers his time-machine has been stolen, he must stop the megalomaniacal thief from using it to take over the world?

Good points written above about the words that makes it shorter!

Maybe the fact that the thief is his friend is important for the turns somewhere in the film but is not important to describe the basic plot?

Possible rewrite

When a irresponsible time-traveller discovers his time-machine has been stolen, he must stop the megalomaniacal thief from using it to take over the entire world...?