I post this in case other supervisors / mentors who care about creating a positive and healthy environment find this useful.

Four years later... I can tell the complete story. This person finished the tasks and left.

Looking back at the facts, I can answer my own question now.

What happened

• I tried to talk again with him. Didn't work, he didn't change a bit his ways. It only got worse.
• He got things done (more on this later). Finished and (fortunately) left.
• I did not, contrary to advice from some colleagues, pursue any formal/administrative action against this person.
• After commenting this to other people (looking for their opinions/advice), it turns out this person had several altercations and problems with different colleagues. From what I heard, it is evident that he has a problem with the figure of authority and does not react well to guidance/mentoring from anyone.

Lessons learned

• The communication style should not be an obstacle, as long as there is a willingness to communicate. @Nik, yes I tend to be lengthy in writing. But I have no problem if someone needs a shorter and to-the-point style, I can adapt to that. This was clearly not the problem here.
• @user35129 your comment that I "sound a little too confident" about my supervisory style and that I "assume that any fault causing the current challenge is due to the student's advertent or inadvertent misbehaviour" is totally unjustified. Did you even read my 2nd paragraph?
• Asking for advice from people I respect was the best thing I did. It gave me multiple views on the subject and helped me to take my decision with more confidence.
• Since this was the first (and until now, only) time I experienced this kind of situation, I also learned about myself: I do not appreciate someone who "gets things done" if it is not within a context of communication and mutual respect (to me and to the rest of the team/colleagues).
• I decided that, while I am the group leader/senior the "he is an ass... but he gets things done" kind of role is completely unacceptable and opens doors to all kinds of abuses, toxicity, and unjust situations. Hopefully, this behavior belongs to a past era of Academia.

My advice

• To students / mentorees: Communicate. Everything else is solvable.
  
• To supervisors / mentors: Stay humble. But don't be hesitant to reinforce respect and communication in the workplace. Don't be afraid to prioritize social peace and mental health over everything else. If you don't have those, you have nothing.

I post this in case other supervisors / mentors who care about creating a positive and healthy environment find this useful.

Four years later... I can tell the complete story.

Looking back at the facts, I can answer my own question now.

What happened

• I tried to talk again with him. Two times. Didn't work, he didn't change a bit his ways. It only got worse and in the end, we only exchanged the minimum amount of emails to keep the project 'operational'.
• He got things done (bare minimum). Finished and (fortunately) left.
• Contrary to advice from some colleagues, I did not pursue any formal/administrative action against this person.
• After commenting this to other people (looking for their opinions/advice), it turns out this person had several altercations and similar problems with different colleagues. Apparently, he has some kind of personal issue with the figure of authority and does not react well to guidance/mentoring from anyone. This was mentioned over and over by a number of his former colleagues and supervisors. Now I think "Gosh, I should have realized this was the issue!"

Lessons learned

• The communication style should not be an obstacle, as long as there is a willingness to communicate. @Nik, yes I tend to be lengthy in writing. But I have no problem if someone needs a shorter and to-the-point style, I can adapt to that. This was clearly not the problem here.
• @user35129 your comment that I "sound a little too confident" about my supervisory style and that I "assume that any fault causing the current challenge is due to the student's advertent or inadvertent misbehaviour" is totally unjustified. Did you even read my 2nd paragraph?
• Asking for advice from people I respect was the best thing I did. It gave me multiple views on the subject and helped me to take my decision with more confidence.
• Since this was the first (and until now, only) time I experienced this kind of situation, I also learned about myself: I do not appreciate someone who "gets things done" if it is not within a context of communication and mutual respect (to me and to the rest of the team/colleagues).
• I decided that, while I am the group leader/senior the "he is an ass... but he gets things done" kind of role is completely unacceptable and opens doors to all kinds of abuses, toxicity, and unjust situations. Hopefully, this behavior belongs to a past era of Academia.

My advice

• To students / mentorees: Communicate. Everything else is probably solvable.
  
• To supervisors / mentors: Stay humble. But don't be hesitant to reinforce respect and communication in the workplace. Don't be afraid to prioritize social peace and mental health over everything else. If you don't have those, you have nothing.