Tobii can say whatever it wants. The license you accept only applies to their software, not to their hardware. You own that. You can use their gaming devices to do research all you want, as long as you use your own software with them.
“The license you accept only applies to their software, not to their hardware.”
As far as I know, their EULA has three groups: gamers, commercial, research.
You can buy a 3000€ research license that simply allows you to collect the eye tracking data on the basic 250€ devices…
Tobii can sue whoever they want, too. You sure you can afford better representation than theirs? If they're as assertive about their license terms as it sounds like they are, I'd think hard about it first, I suppose.