* I have Kaspersky's security suite installed on the computer - but it's only activated for virus protection and even quitting this completely makes no difference.
As these utilities I believe install kernel extensions onto the Mac, I am wondering if there is something in Kaspersky that is blocking that IP address? Since your iOS device within the WiFi network can get to the site, that rules out something on the routers or blocking by your isp. And since I can get response to the site from Mojave, it’s not something specific to MacOS.
(If you are able to use a hotspot feature through your mobile carrier from your iPhone or an LTE iPad, that’s another way to isolate the system from your network - create a temporary hotspot to the phone or iPad and try the ping to see if it gets through. That would isolate seeing if it’s a network issue.) But, I don’t think that’s it. I also wouldn’t bother trying to connect the iMac through the isp router/modem at this point. That’s too much bother for what I think the issue may be.
I’d strongly suggest at least completely uninstalling Kaspersky and restart the Mac to see if that changes anything. You can always reinstall the suite if it makes no difference. It may not be Kaspersky, but those security suites do install a bunch of system stuff to try to protect you. I’m wondering if it’s over-protecting in this case.