First off, the film opens on a screen split four ways. Immediately the audience knows this will not be another typical romantic-comedy or action fare. Like, for sure. What Figgis is trying to do by placing four mini-films into one goes back to an old cinematic technique called montage.
Montage basically juxtaposes two images against each other to create a new meaning.
Real-time simply means that time in reality equals time in the characters' reality. Watch this film, if only to see something exciting and new, while you wait for those life-changing votes to come in.