Your average everyday Existentialist philosopher might have a few criticisms of the Old Man. In the Existentialist view, our lives have no purpose, making everything we do ultimately absurd. This means that people must decide for themselves what is meaningful – we must take responsibility for our own actions and existences.
The Old Man seems to have never really taken responsibility for anything and constantly blames his wasted life on other people. He whines to the invisible Emperor, "I wanted to climb stairways, they rotted the steps...I fell down...I wanted to travel, they refused me a passport...I wanted to cross the river, they burnt my bridges..." (447). An Existentialist might tell him, "Too bad, buddy. That's the way it is. You should've tried harder."
Also notice that the Old Man has never committed to any particular profession. His wife is constantly reminding him of his wasted potential, telling him things like, "You could have been head president, head king, or even head doctor, or general, if you had wanted to, if only you'd had a little ambition in life" (16). The Old Man's only comeback for this is, "I am a general. [...] since I am a general factotum" (17). A general factotum is a person who does a little bit of everything around a building. So we see that rather than committing to one particular thing, the Old Man just does a little of this and a little of that. His life has never really amounted to anything, because he's never really tried.
Of course, the Old Man claims to be very committed to having his great truth-bringing message heard by all humanity. Given this, you could choose to see him as a good Existentialist. The Old Man claims to have been working on this message his entire life, so perhaps he was committed to something he thought was meaningful. Now, in the face of an absurd world full of invisible people, the Old Man is determined for his dream to be carried out. He's taken responsibility for the fact that he's a bad communicator and has hired a professional Orator to speak his message for him. When the message is delivered the Old Man will not only bring meaning to his own life, but to the lives of all humanity. When he kills himself after the arrival of the Orator, it could be seen as the ultimate act of taking control of his life. He's achieved the goal he set out to achieve, and now he's ending his life in a way of his own choosing.
That's a pretty good argument, but there are still a few problems from an Existential perspective. First off, there's a high probability that there are no invisible people and even no Orator. It could all be a fantasy. The Old Man could be just inventing this whole scenario to avoid taking responsibility for his wasted life. Even the message could be a fantasy. The Old Man says he's hired an Orator because he's a bad speaker, and yet he gives a long speech just before the Orator is to deliver the message. Then the Old Man kills himself without waiting to hear the message delivered. We think this is all pretty fishy. If the Old Man really has a message why doesn't he just deliver it himself? Is this just another example of the Old Man shirking responsibility? Does the Old Man kill himself because he knows that the Orator has no real message to deliver? His suicide could be seen as the ultimate act of cowardice. Instead of facing the hash realities of life, perhaps he chooses to run from them.