Blender is the application and Cycles is the render engine.
Studio itself is a Unity application that would almost certainly be incompatible almost in its entirety with any source code they could pull from Blender. At that point they would be porting logic.
Their Eyesight renderer is a separate application that looks to be a fork of Blender with everything but Cycles pulled out. COPYING.txt explains that Eyesight is based on Cycles using the Apache License v2.
C:\Program Files\Studio 2.0\PhotoRealisticRenderer\win\64\license if you're curious.
Not that it excuses them necessarily, but Studio was not created by LEGO. Bricklink was purchased by LEGO relatively recently and had no say in its development. It is very likely a small team built it not even thinking about legalities.