~は~で ishas a little broader usage than "in one's own way". It's used when the process/reason/method is different but the essential result/conclusion is the same.
- これはこれで美味しい。
This is delicious in its own way. / This tastes different from the previous one, but still is delicious. / This taste is not what I initially expected but it's delicious anyway. - 彼は彼で頑張っている。
He is trying his best, too (although he may not look like youothers). - 今日は今日で忙しい。
It's also busy today (for a different reason). - これはこれで問題だがある。
This (suggestion) is equally problematic (although I understand the approach is different).
Likewise, this あいつはあいつで is therehere to make thea contrast between the narrator (who is thrown in the air) and the friend (who is lying on the ground). They are seemingly placed in different situations, but the ultimate result is the same; they are both dying while looking at each other.