Is the dynamic programming pairwise alignment algorithm considered greedy?
No. Rather, the DP algorithm for pairwise sequence alignment1 is an instance of backtracking. What makes it superior to naïve exhaustive search is that


it abandons potential solutions as soon as it can prove that it is going to be sub-optimal (each field in the DP matrix considers only the optimal previous sub-alignment), and
it computes partial results only once and reuses them — that’s the “dynamic programming” aspect of it.


There are other, greedy algorithms for pairwise sequence alignment. These will first find so-called perfect “seed matches” between a query and a database, and then extend those outwards using one of several strategies. They thus explore locally optimal solutions but aren’t (in general) guaranteed to find a global optimum. This is for instance what the BLAST algorithm is doing.



1 By which I’m assuming you mean the Needleman–Wunsch or Smith–Waterman algorithm or some minor variation.