"Stand back, I'm going to try science!"
Based on experimental results, it seems that the claim made in the question above (namely, that all comment flag types effectively count as delete votes) is only partially correct. Let me try to summarize the results below:
Confirmed for one-flag instant deletion: Comments containing certain keywords (one confirmed example being "accept rate") are immediately deleted when any flag, including "other...", is raised on them.
Disproved for normal auto-deletion: Four to six "other..." flags on a comment containing no instant deletion keywords do not seem to have been sufficient to delete it. In a follow-up experiment, three "too chatty" flags were sufficient to auto-delete a comment, while the same number of "other..." flags were not.
Here are the details of the specific experiments carried out. I have made this post community wiki, so feel free to add your own results:
Procedure: The following comment, posted to the question above:
Why not test for ourselves? Please, flag this as "other" write "test, please ignore" and see if and when it gets auto deleted. Anyone flagging please acknowledge by a comment. – Shadow Wizard
was flagged as "other..." by at least four users within a span of slightly over two hours, and by two further users within approximately 14 hours.
Result: As of this writing, the comment remains visible.
Conclusion: It is possible that "other..." flags may not contribute to normal comment auto-deletion. However, depending on the number of flags actually needed for auto-deletion, and the unknown variable of moderator activity, an alternative explanation for the result that the number of active flags on the comment may never have reached the auto-deletion threshold. Further research is needed to rule out this possibility.
Further research: To eliminate the unknown variables in this experiment, it would be desirable to repeat it with two consecutive comments, one asking to be flagged as "other...", and the other asking to be flagged as, say, "too chatty". It would also be desirable to coordinate the flagging, say, on chat, so that at least half a dozen flags could be reliably cast on each comment within a short timespan. Finally, we should include a note in each comment asking moderators not to dismiss (or accept) any flags on these comments within a certain timespan.
Procedure: This experiment consisted of several phases:
Based on rumors that comments mentioning the words "accept rate" may be deleted with a single flag, a number of such comments were located on SO with a Google search. Among these, a few were flagged as "obsolete", and were observed to disappear instantly.
Having confirmed that "obsolete" flags on comments containing the keyword "accept rate" did trigger instant deletion, the same procedure was repeated with "other..." flags. Again, the flagged comments were observed to disappear instantly.
Finally, to confirm that this behavior is not limited to SO, a comment (since deleted) containing the words "accept rate" was posted to the question above here on meta.SE. A single "other..." flag was cast on this comment, which was observed to disappear instantly.
Result: All flagged comments containing the keywords "accept rate" were immediately deleted, regardless of the flag type.
Conclusion: At least for comments containing instant deletion keywords like "accept rate", flagging as "other..." appears to trigger immediate deletion.
Procedure: The following two comments were posted on this answer:
Test comment A: Please flag this comment as "other...", with the text "test, please ignore". Mods, please do not dismiss, accept or otherwise act on any flags on this comment before 15:00 UTC (approx. 1 hour 40 minutes after it has been posted). Thank you for contributing to science!
Test comment B: After flagging the previous comment, please flag this comment as "too chatty". Mods, please do not dismiss, accept or otherwise act on any flags on this comment before 15:00 UTC (approx. 1 hour 40 minutes after it has been posted). Thank you for contributing to science!
Users on meta.SE chat were requested to flag both comments as described in the comment text.
Result: After three flags on each comment, comment B (flagged as "too chatty") was deleted, while comment A (flagged as "other...") still remains.
Conclusion: It appears that, indeed, "other..." flags do not count for normal (non-instant) comment deletion, or at least that, if they do, the threshold must be higher than for normal comment flags.