While they won't really matter, for academic purposes:
Engine Clock is the frequency the GPU itself runs at, similar to CPU clock rate.
Memory Clock is the speed the VRAM runs at. The faster this is, the more memory can be moved at once. This is actually often a limiting factor of a GPU at high resolutions. GDDR5 can run in dual or quad modes, which is why it also lists the 6.0Gbps, since this is running quad.
Memory bandwidth is the effective memory clock multiplied by the memory bus width. Higher bus width or higher memory clock makes this number bigger. At high resolutions, this number alone can differentiate some cards, but you can't rely on it.
Compute units is just a fancy AMD term for a block of GPU "Stream" Processors. There are 64 stream processors per compute unit, and each stream processor can do a "thing" per clock (to grossly oversimplify). Extra Compute units are almost like "Cores" for a CPU, except they can do the same thing in bulk (in this case, 64 times per clock) with each stream processor.
Texture units are "cores" of a processor set up specifically to handle texture-based math as efficiently as possible. More of these means more texture processing.
ROPs, or Raster Operators, tend to do per-pixel operations, whether this is post-processing or determining what color each pixel should be from the mess of 3D objects with transparency, lighting, bloom, etc. that the rest of the GPU generates.
Not sure on Dual Geometry Engines past AMD marketing buzzwords. You see it a lot but never and explanation of what it means. Possibly it has the capability to render two unrelated scenes at once or something.
As to the "scale" at which they matter, it's safe to say at a very minor one (except Memory Bandwidth). They tend to be designed with as much balance as possible to prevent any transistors from idling. In the original GPU's, You would have something like a compute unit attached to exactly one texture unit with exactly one ROP on the end, but that left the GPU sitting idle much of the time. Additionally, Texture Units and ROPs are more or less useless for direct compute functions and wot. The reason why they don't matter is because there is a massive difference in the efficiency of these parts between GPU's, and while these parts are the reason why some games favor some GPU's over others, nothing in these numbers can actually tell you which GPU is better.
Though if there's a significant difference in Memory Bandwidth, that's a pretty good tip that one of those chips is considerably faster. You'll still have to look at benchmarks to know how much, though, so honestly, you may as well start there are save yourself time, and treat those other numbers like the marketing buzz they are these days.