I think we should consider which cognitive abilities would allow for a mode of communication that would be useful to us as humans. I am not sure if the terms "more evolved" or "less evolved" are helpful.
Human language has the ability to express abstract ideas. I can describe something to you that you have never experienced yourself. I can explain my perspective to you and how I feel about something even if these are things you have never experienced yourself.
This seems like an ability that would be important for an alien species to have in order for humans to have a meaningful interaction with them.
There are many animals on Earth that have modes of communication that are inaccessible to humans. Ants communicate a lot of information with pheromones, and bees do a crazy little butt waving dance. Humans can try to replicate the butt waving dance... but what we are doing has nothing to do with bee communication. So sure... these aliens (just like ants and bees) might have some form of communication that relies on cognitive function that humans don't have and is beyond the ability of humans to use. This seems rather irrelevant. An alien that relies on some cognitive function that humans don't possess would be just as impossible to communicate with as ants or bees.
If humans are to have a meaningful conversation with some alien species, then this alien species has to have the specific cognitive abilities that will make this possible.