Everything works as expected with the Mac wired to the router so I would think the firmware is compatable.
It's only when the Mac is using the WiFi adapter to connect to the router that there is an issue.
Will look at router WiFi settings.
Give everything a fixed ip and make sure you can ping all devices. Fixed ip on your computer too. If everything is setup properly it shouldn't make a difference but it's an easy test and if something changes then you've got another data point.
BTW, macs do have a firewall. Probably not your problem here but check to make sure it's disabled just in case.