It is a normal backpack, and it doesn't have any wheels. Certainly I would not expect a rollaboard type bag to be allowed as the personal bag.
Ideally I would like to find a backpack at exactly the Aer Lingus dimensions, as everything I have found so far is either really tiny, or is a couple of centimetres too big in one direction or the other. I realise that a backpack a couple of centimetres too big is unlikley to be noticed, but I would rather stay within the limits so it is not open to challenge.
I understand. Im having the same problem concerning the same airline. I saw on one site that roller cases could not be used under their seats. I'm like you, I plan to use a backpack type bag but it is longer than the size I've found for that airline. I hate to have to pay for a 15 or 18 inch long bag. The width and depth of my bag size is fine. My son keeps telling me they never check it but everyone will know it's not the right size if it doesn't fit under their seats.