What is the meaning of DISTINGUISHED in a given context?

You should scroll down to the middle of the same page. Where it reads, English Language Learners Definition of distinguished

known by many people because of some quality or achievement.

So, the agent in the given excerpt lacks the quality of selecting proper vocabulary.

To be "not particularly distinguished for the range of choice of his vocabulary" means he is not a wordsmith. He doesn't possess, or in conversation does not express a wide variety of words. Consider someone who uses 'very' to describe a wide variety of situations or experiences (e.g., 'very good', 'very tasty', 'very late'). A person who is distinguished for his range of choice in his vocabulary might instead use adverbs such as 'extremely', 'exceptionally', and 'vastly', or adjectives such as 'particular', 'exceptional', 'remarkable'. A person who is not particularly distinguished may only use the word 'very'.

As you have rightly pointed out DISTINGUISHED is used here in the sense KNOWN FOR or FAMOUS.

You can find the desired meaning in the Thesaurus portion of Merriam Webster online where in serial number (2) the meaning is: " standing above others in rank, importance, or achievement"