Cards are, IMO, not a great randomizer mechanic for an RPG, in a miniatures game they are awesome, but the same is not true of an RPG. Knowing what cards you have drawn, and possibly seeing a control hand as well, will cause inaction amongst players who know they are in for a bad draw, the same way difficult rolls, with serious consequenses, stifles creativity in other games. A die does not have a memory, you could roll nothing under 10 on a d20 all night, but it will average out over time, a deck on the other hand does have a memory thereby introducing the knowledge that you WILL draw low sometime during the session. Using dice WITH a control hand does however give you a randomizer and a way to cheat Fate without worrying the card-counters.
This part:
is what I'm curious about, as it could be read in any number of ways, from "you don't need minis but you can if you want" to "you only need them during combat" to "you need them but we think it works fine".
Of the 6 games listed, I have 5 in my bookshelf, the 6th being D&D. Of the others, 4 don't use minis (though you could if you wanted to), and WFRP uses standups but measures distance in such an abstract way that it is equally easy to use a page from a notebook to keep track of combat.