Yes, the Stefan-Boltzmann law is the more fundamental one (it applies to all objects that behave as blackbodies, which is good approximation for all stars), and it is so important in astronomy and physics that it really shouldn't have needed to be justified. Your observation of the error was correct.
We can also make the calculation a little more simple when we know the star's temperature and its radius in solar units. Then the luminosity in solar units is
Consider a star 6 times the radius of the Sun, with a temperature of 29,000K (about 5 times the Sun's temperature of 5800K). Square the 6 (that's 36) and raise the 5 to the 4th power (that's 625). Multiply 36 and 625 together, and that's 22,500 times the luminosity of the Sun. (The star you posted in the OP is a little bigger and a little hotter so it is even more luminous than this.)
I'm not sure of the cause for this error. I looked in earlier versions and could not find it in any O or B stars -- their luminosities appeared to be perfectly consistent with the Stefan-Boltzmann Law. I'll make sure that this is brought to SpaceEngineer's attention. Thanks for reporting it!