Similarly Frank Tipler limited his claim, "Extraterrestrial intelligent beings do not exist" (Royal Astronomical Society, Quarterly Journal, Vol. 21, Sept. 1980, p. 267-281) to the Milky Way galaxy.
An answer to the question of whether the Milky Way galaxy is the only one with extraterrestrial intelligent beings will include the same factors which likely limit the number of Milky Way planets with intelligent beings to approximately one.
In addition there are also the other factors, such as whether there are unique galactic features necessary for intelligent life (regardless of whether they have the capability of intergalactic travel) to exist within that galaxy, which are only found in such special galaxies as the Milky Way, e.g., the size and shape of the galaxy, the size and activity of the galactic center black hole, the abundance and distribution of other black holes within the galaxy, the frequency of collisions with other galaxies, the amount of dark matter present.
An answer to the question of whether the Milky Way galaxy is the only one with extraterrestrial intelligent beings will include the same factors which likely limit the number of Milky Way planets with intelligent beings to approximately one.
I said that my QUESS is: one human-level-intelligence per galaxy, on average.
It would explain why our galaxy so far is generating questions like the Fermi Paradox... because WE are the one intelligence in THIS galaxy.
Just my opinion, of course. But I am ever-interested in this issue and always enjoy discussing it.
With regard to red dwarf stars, my GUESS is that almost none of them harbor much in terms of complicated evolution, but I PREDICT that those intelligences (hopefully we are one of them) that do achieve star travel will end up colonizing planets around red dwarf stars, for the simple reason that those are the stars that will still be around — and still be pumping out heat and light — HUNDREDS of billions of years from now.