I think it's about someone committing suicide, with a few hints of an existential crisis. The singer alludes to the day being a "This bleak whiteness, nothingness", and the "The eye that stares through your mirror" as perhaps his soul staring at himself.
Him in his dreams being older alludes to how some dreams have you dying, and those dreams being close to dying yourself - hence being older used as a similar meaning. The singer saying "This could be New York, This could be London, I don't care anymore" is him talking about how his surroundings don't matter, which make him feel bleak about his future.
The segment that comes after about him being in a black suit, black tie, could allude to funeral wear after he kills himself, or it could alternatively mean his bleak routine at work (he says he "must go to work" later on). The "piano that falls from above and smashes in front of me" refers to how close he was, or is, towards death.
Finally, the last segment, "I see two figures asleep, They look older, You look older, We're all older" refers to the future in where he's dead. It makes even more sense when he says after that "Let us join them in their dreams", which obviously means that he'll kill himself and join the dead in their dreams, which also ties in with his previous dreams where he's older. The final part, which name drops, states that "We're only four hours, We're only four moments", talks about how people are on the earth for a short amount of time, in his instance, 4 hours. It takes 4 hours to kill himself, and 4 moments for the action to be done.