Words like "circumvent" and "environment" are close in regards to complexity. Words like "us" and "me" are close in regards to complexity.
The counting argument tells us that most strings are not compressible. It is then a wonderful feature of sensor data, natural language, DNA and computer code that it can be compressed quite a bit. This means there is a certain order in the language that compressors can use to keep the file size smaller.
There is a cognitive economy trade-off between the energy needed to keep a system running and increased complexity. Less complex language helps us save energy. We use short words for concepts that we use often. Very complex concepts and words like "disambiguation" may be described with shorter simpler words to someone who has not stored that word and general accepted meaning yet.
In this complexity view languages evolve to use as little energy/computational complexity to convey as much information as possible. The results found in this article can also be explained using this view. Parsing a sentence like "Throw the trash out" requires you to store in working memory the word "throw" 'till you get to the word "out" for the full concept "to throw out". Until you get to the word "out", the "throw" remains in a superstate (could become "throw in", "throw on" etc.). You need both words to form a mental picture of someone throwing out the trash. This requires more computational energy to the listener, and is hence ineffective. If you want your message to be heard, you have to communicate in clear simple-energy sentences. So using simpler less computationally intensive sentences benefits both the speaker and the listener.
This would readily explain why natural languages beat the random benchmark. Randomness has far less structure to use for compression by an intelligent agent. Randomness is not optimized communication, since it is more unpredictable.
In short: Simplicity and conveying information with little energy is a fitness factor that natural selection optimizes for. This is universal to all natural language speaking agents with a limited energy budget.