German researcher suspects that only Earth-sized planets may be able to have life

You can read about this at New Scientist here. The general idea is that only planets of about our mass are capable of having the right plate tectonics, as well as super-Earths possibly not being able to have a magnetic field.

This could be true, though also note that predictions about what isn't possible are much harder to make than those about what might be possible, as this famous example shows where an otherwise intelligent professor concluded in 1887 that flying machines were simply impossible. Also, we don't even know for certain that life can only exist in a carbon-based form, what its limits are, etc. And moons orbiting gas giant planets are in a different situation entirely, with a lot of heating being created by the interaction between the moon and its planet. I'm not sure if he has included these types of moons in the equation too, or whether it was limited to planets orbiting stars.

Also note that when the article speaks of planets with an Earth-like mass it means those from 0.5 to 2.5 times our mass, which is still a fairly large range. Venus is 0.815 times the mass of Earth so an astronomer looking from outside the solar system working on his assumption would conclude that there were two planets that might have life here.