I'll be honest, I'm stumped.
When I pulled up your post, I initially saw what test/passage it was and just started reading the passage (having not yet seen your question).
And just like you, I was completely befuddled by the explanation of the basalts. I re-read the 2nd half of the 3rd paragraph like 3 times, because I couldn't figure out HOW they were trying to make their point.
For the sake of getting through the answers, we at least know that "showing different alignment = evidence for drifting", but why it does is unclear to me.
It seemed to me like they were saying, "Since basalt takes a permanent snap-shot of the magnetic field when the basalt is formed, basalt formed at the same time on the same continent should show the same picture of the magnetic field."
Okay, makes sense.
"But .. basalt from North America formed at the same time as basalt from Europe shows DIFFERENT pictures of the magnetic field."
Okay, groovy. So we can infer that those basalts were NOT on the same continent.
That much makes sense to me. But how does "not on the same continent" provide evidence for continental drift?
It seems like if you DIDN'T believe in Pangaea or continental drift, you would just say, "Of course their basalts look different -- they're different continents. That doesn't mean they started out as the same continent and then drifted apart. It could just mean that they were always apart."
Since these RC passages are edited down from their original texts into appropriately short excerpts, I'm wondering if some crucial sentences were left out ... or if it was just sloppy writing ... or if we're really just missing something.

I actually thought I had heard this story before, told differently, as evidence for Pangaea.
If you say "basalt formed at the same time on different continents should NOT look the same" and then say "basalt from an early epoch on North America looks the same as basalt from the same epoch on Europe" then you can infer "Whoa, so during that epoch, North America and Europe were the same continent!"
This, to me, is strong evidence for continental drift. By establishing that these two, now separate, continents were at one point on the same continent, you can infer that they've drifted apart.
Anyway, sorry I can't be more illuminating.