It does seem poorly translated, doesn’t it?
Looking at the Chinese (https://law.moj.gov.tw/LawClass/LawAll.aspx?PCode=D0030001 ):
First thing you notice is that there’s no explicit ‘shall’, a character like 屬 is used for ‘shall’ in other articles.
A layman’s reading: “ROC Nationals having one of the following circumstances, with to the permission/approval of MoI, (can) forfeit ROC nationality:”
Logically, the three articles are times when a ROC national may want to give up ROC citizenship. They’re all times when having ROC citizenship could prevent you from obtaining another one you want to obtain.
This is further backed up by Article 15 - which says (approximately) that you can get your ROC nationality back if you lost it due to Article 11 (if you meet the requirements).
Article 13, to a lesser extent, also fuels the logical argument. One way to read it is that as a list of times when ROC won’t let you renounce citizenship under Article 11 (because you’ve been bad and might be trying to escape justice).