As Netibiza's post indicates, the 'Trunki' easily complies with the size restrictions which are imposed by security staff (and are common to all departures from all EU airports).
Some airlines have restrictions which impose lower limits, due the size of the overhead lockers on their aircraft. However, the Trunki seems to still fit well within even those lower limits.
I'd never seen (or heard of) a Trunki until a few weeks ago, when the family ahead of me in at passport control in Stansted airport had a little girl who was riding one. They'd just got off the same Ryanair flight as me, with the Trunki as hand luggage. Given that Ryanair have the smallest dimensions for hand luggage that I know of, and also given that they usually apply them very strictly, it would seem to suggest that no airline would have any problem with carrying a Trunki as hand luggage.
Chris