Yeah it looks like that kit is designed to use an external power supply. Which they just so happen to also offer apparently, going by the description. That would likely use a tube as well. What kinda confuses me is the two connections for 260v, since it's a three screw terminal block. Dunno if that means it wants two 260v supplies out of phase with one another or what. The schematic is too low quality for me to read all of the text. Either way I'm pretty sure it means the step-up transformer would be at least 520v, center-tapped, giving + and - 260v. Then it'd be smoothed out and rectified. Pretty much any tube amp is likely going to be a high voltage like that. Dunno how low they can go for sure.
On the bright side, those are triodes, so it is in fact a true tube amp.