Cast Away actually has two characters on the island-- Chuck Noland and Wilson (the soccer ball). Even though Wilson cannot talk, Chuck voices the alternative perspective to his own. You'll notice that time on the island is equally spent between the four throughlines. Stranded on a deserted island is the OS throughline. Obsessed workaholic is the MC. Stoic sidekick is the IC. And the strained relationship is the RS. So, even though there isn't another PERSON on the island, the storyform necessities are nicely handled.
I suggest that you do the same for your one character piece. The "other" can be the character's absent parent, teacher, child, boss, or whatever. Just make sure that IC perspective (in fact, all four perspectives) are communicated.
Whether you have one player or one-thousand players, you need to communicate the four throughlines to your audience. The throughlines form the basis of your airtight argument (if, in fact, your intention is to create a Grand Argument Story [GAS]).
With two players, it's easy to tell a GAS. One is the MC. The other is the IC. Their relationship is theRS. And the larger scenario in which they find themselves is the OS.
You can have one player describe all four perspectives if you want. For example, the MC might say, "You know, your problem is that you're bias blind's you to obvious flaws in your logic (IC=Fixed Attitude). Sure, I'm stuck in a rut and can't seem to get out (MC=Situation), but that doesn't explain why we have to play games with one another instead of just recognizing the fact that we're meant for each other (MC/IC=Manipulation). And if you don't get up off your ass and start shoveling this stuff, that foreman over there is going to ship our asses off to some worse work camp (OS=Activity)."
You see, the number of players does not limit your ability to express any or all points of view in your story.