As Danack said in comments, there are 2 php.ini files. I uncommented the line with curl extension in the one in Apache folder, which is php.ini used by the web server.
Composer, on the other hand, uses php for console which is a whole different story. Php.ini file for that program is not the one in Apache folder but it's in the PHP folder and I had to uncomment the line in it too. Then I ran the installation again and it was OK.