Citing own work within a paper and being anonymous
If this is in the context of double-blind reviewing, the correct response to this situation is to alert the handling editor or PC chair to this situation. Different venues are differently strict about double blind reviews, so the response to the situation may vary between "well, we don't care if the authors wants to reveal himself" to a reject and resubmit (without the incriminating statement and a new set of reviewers). However, which of those it is is not your decision as a reviewer.

If this is not in the context of double-blind reviewing, you are aware of the identity of the authors anyway, and this statement gives you no additional information.

If you are just reading the paper (and not reviewing), as implied by the wording of your question, then I don't understand the issue. Published papers generally have publicly visible authors, and it is not clear that the incriminating wording was already visible during review. For instance, in many software engineering venues that nowadays use double-blind reviewing, it is customary to "blank" self-citations and to slightly change the phrasing for the review version to make sure that identities are not, or at least not obviously, revealed. This can then be changed back for the camera-ready version.