Hello, hadi…. while this isn’t strictly related to WP (since unfortunately there are no plugins for WP which will produce this sort of directory), I use a nice script which produces clean code (though not tableless unless you use either my template or kickass’s for it): https://www.phplinkdirectory.com/
One thing up-front: while the authors of this script “seem” to be within the open-source community effort, they spend a lot of time pimping for dollars for fixing things, adding things etc. No one minds a donate button or so, but sometimes constant begging is pretty objectionable. This sort of thing is overweighed however by the usability of the script itself.
