I think that definiton is a little bit flawed.
I wouldn't see it as an either or. Most procedural shows have serialized elements,
The Last Ship seems to be in the middle.
Each episode has its own primary problem, but they also build on each other.
The last ship, going by that definition in the link, is certainly a procedural.
The second episode was the exploration of Guantanamo Bay. The third was the stand off with the Russians. This fourth episode was a water seeking thing. They could be watched in any order and still make sense (ignoring the pick up of the guard from Cuba).
Hence, procedural. No?
It is not just the guard.
Goegraphly they arrived at Gitmo in episode 2 and episode 3 happened there as well.
The damage that caused the problem in episode 4 happened because of the events episode 3. We got a spy in the first 2 episodes, who was revealed in episode 3 and starts to become reintegrated in episode 4.
There are ongoing problems among the characters.
And I guess episode 5 will lead to new research, which will lead to to a new event/adventure