It should be noted that train tickets departing from DUS should actually always be purchased in advance, for two probably not too obvious reasons:
First of all, technically, you will need to be in possession of a valid ticket for the people mover between the terminal and the long-distance railway station (although my ticket has never been checked on really numerous rides), and you cannot really get a proper ticket at the airport (they only sell tickets for local transit, which I think would be too complicated for any visitor).
And then, there are only 4 ticket machines at the airport station, which are quite circumstantial to use (even if you use them on a daily basis) and are hence usually occupied by desperate, newly arrived people who don‘t really know how to use them (and there‘s nobody there to help then). It‘s actually quite likely that you‘ll miss your train due to the wait at the ticket machines.
So, always buy your ticket in advance when traveling via DUS.