No, thats not a tracert, thats a Pingpath, or something similar. Judging from window, Im assuming linux?
Eitherway, your data is showing repeated, but intermittent, packet loss of over 50% between your computer and router. Its probably random enough that sometimes when your testing, its fine, and other times, its giving the packet loss. Thats probably creating the illusion that its only to some sites. Thats why I asked you to bypass your router. You keep repeating you modem is connected direct to the wall, but thats coaxial. I mean plug the ethernet from the computer direct into the modem, bypassing the Asus router. Then try a exstended ping, from terminal
Ping -c 200 cox.net
For more info see here. By the way, what distro do you have? Im not much of a bean, but I love to learn.