Because he is still writing, he isn't done, he is still doing it, so you have to use present.

if you use "does", that means he 'always' writes and it wouldn't be true because he started to write in the morning and maybe he will finish soon. He won't continue after it finishes typing. if you use does, that means he will continue to write after finishes, he will continue to write every day. That's not a routine, that's not like i "do" take a vacation every summer. that's like i'm having breakfast right now and after finish i won't continue this.