Which cases are unlocked by the Gigabyte GTX970 mini-ITX card?

Quick answer - very few.

It's actually very puzzling why multiple manufacturers are pushing "ITX" graphics cards on us as right now they make almost no sense. For a start, ITX graphics cards aren't a standard so there isn't any guarantee that an "ITX" card will fit every ITX case. If it was a standard, most likely it would be single slot to match the mini-ITX format. I guess it's partly a case of chicken+egg - if there are cards on the market then case support is likely to increase.

Far more interesting than short cooler cards (which is all these are) would be powerful low-profile cards to match a case like the one SproutSchon linked, or a return to single slot cooling. Both of these have significantly more potential for size benefits in a mini-ITX scenario.

Unlike some of the other cards on the market the Gigabyte model does have one thing going for it. Gigabytes "standard" high end Windforce cooler is enormous so it probably makes sense for them to cover the market as best they can with an alternative model with greater case support.

To directly answer your question, there's quite a lot of m-ITX cases which do not support "full length" (again, a non-standard, can mean anything) cards but the vast majority of these are not limited to anywhere near the 170mm of ITX motherboard size. The Lian Li PC-TU100 is a popular travelling case due to the handle and reinforced edges, max graphics card length = 193mm. Lian Li PC-Q33 = 220mm. Elite 110 = 210mm. All of these can't fit a reference Nvidia cooler (perhaps the closest thing to a standard atm) but none of them explicitly need a 170mm card. There's traditionally been a very good selection of everything up to mid-high end of cards which fit in these scenarios.

Bit of an aside, but part of the reason for this is that the GTX670, GTX660Ti and GTX760 all had a ~170mm reference PCB. The stock coolers extended beyond this, but plenty of manufacturers produced used it to their advantage.

I kinda disagree that the Prodigy/Phenom benefit from a 170mm card. What a longer card collides with in a Prodigy isn't so much the HDD cage but the HDD trays. It's actually a slightly silly issue - Bitfenix could easily offset the cage slightly to avoid this and you can wiggle things around if you desperately need stuff to fit.
Thing is, I don't think I've ever seen a picture of anyone using the upper HDD in a Prodigy. With it removed there's still space for a full sized ODD, two 3.5" drives and four SSDs which covers an awful lot of scenarios.
I actually use a 180mm long GTX660 which means I could use the cages if I wanted.