Even Microsoft calls it the system tray (see as an example https://learn.microsoft.com/en-us/windows-hardware/drivers/a...)

That guy's got a problem with his entire company, and their documentation. If he can't get over it, he should clean house first and only then try to police what the rest of the world calls it. As long as MS insists that it's the system tray, people are going to call it that no matter what his team wishes it were called instead. Renaming systray.exe would be a good first step.