"Am I a coward or a tactician?" "A tactician. A tactician, surely."

Indefinite article needed. Also the last two sentences would seem to be uttered by the same person, so should go within the same quotes.

Wouldn't you omit the article in a laid-back conversation? (Perhaps you wouldn't, hence I'm asking.)
It's from the old chat.
The last two sentences belong to two different speakers (responding to the same question by another speaker - or rather "writer", since it's from an Internet chat.)

The article may indeed have something to do with the level of informality, but I think most English speakers would use it. Articles can be a puzzling problem for people more accustomed to languages that don't emphasize them or, in some cases, don't even have them. The sentence "I'm a doctor, not a tactician" is normal English (from Star Trek) but the French equivalent would normally not use articles, even though these do exist in French: "Je suis médecin, pas tactician." Esperanto has no indefinite articles, so it would have to be: "Mi estas kuracisto, ne taktikisto."