It's clearly confirmed that galaxies don't obey the known laws of quantum electrodynamics (QED) + general relativity (GR) if we assume they are made entirely of Standard Model particles. So, either QED is wrong (extremely unlikely) or GR is wrong (unlikely) or there is some matter that is not in the Standard Model (plausible).

Dark matter corresponds to option 3 - and there are observations that conform some models of dark matter distribution that match quite well between different galaxies. There are other theories as well, such as MOND (modified Newtonian gravity) that explore option 2 (GR is wrong).

Still, whatever the theory, it's clear that what is not happening is "aliens someone consuming all of the EM radiation from some stars". With anything resembling currently known physics, it's impossible to "consume" EM radiation in this way. Electric charge is always conserved, electrons and quarks don't disappear just because they move around, even with something like controlled fusion. A Dyson sphere would be an extremely hot visible object, not some dark point.