This answer is a little more involved than it seems, a tube in a DAC may serve one or more of several functions, as an amplification device to boost the signal to useable levels, as a buffer so that the DAC can drive cables, and as part of a filter to get rid of the noise we don't want. It can also be used to intentionally colour the sound, though I have a very low opinion of manufacturers who do this.
As for why tubes are used, they have two main advantages over most solidstate devices; a high slew rate and lots of voltage headroom. The raw signal coming off the DAC chip itself has a spectra going well out into the MHz range, this necessitates a very fast analog stage to prevent slewing and the subsequent distortion and loss of information. The typical opamp chip used in audio has a slew rate of maybe 10-30V/us, this is not nearly fast enough to avoid slewing. A half-decent tube stage will have a slew rate of well over 100V/us, usually several hundred V/us, a full order of magnitude faster, this is what's needed to pass the signal through without distorting it.
It is possible to build a high-speed transistor stage for a DAC, however this is not a trivial task and not many can successfully implement it. The first of two choices is to use video driver chips, the problem here is that most of these chips have mediocre noise specs when used in audio and they're rather temperamental to work with. The other option is a fully discrete transistor output stage, unfortunately designing one is again something which few audio engineers are familiar with, it's more in the domain of instrumentation & RF designers.
So to summarize, the reason for using tubes is because it works, and it's a solution which is reasonably simple and easy to implement.