When a card's text talks about the members of a party consisting of a rogue, a cleric, a warrior and a wizard what defines each of those party members?

Their creature type line.

It bothers me considerably that there aren't any tank classes in that party line up.

I mean...
1) There is a warrior. Clerics and wizards can be that too, depending on their spells.
2) Normal tank classes are honestly a pretty unrealistic concept. Most enemies will strike to kill - it's much easier to evade earnest attacks than to consistently survive them. And it's far from obvious that wearing armor and being big and buff does better than being divinely blessed or surrounded by arcane force field. And who would WANT to be a damage sponge in the middle of the fray anyway? And how would ONE person consistently prevent enemies from ignoring him and going for the real threats? Can taunting be expected to work consistently? Maneuvering might work alright in the dungeon corridors but won't do much in the open field.

I am confused by the idea that there is a lack of tanks because that is the classic warrior/fighter role. That said, 'tanks' are more of an MMO concept that has moved back into tabletop RPGs. It's not an inherent part of an adventuring group, imo, beyond "big strong person" and it's not native to D&D until Fourth Edition introduced tanking mechanics (marking).