TL/DR version: tempogain is probably right.
The link to the Nationality Act at the MOI's website isn't working for me (typical Taiwan government website!), but I've just checked the MOJ's database and found it, plus something interesting.
Conscription Regulations for Naturalized Aliens & Returning Overseas Chinese
These Regulations are duly enacted in accordance with Article 23 of the Conscription Law.
(Actually the official translation of "兵役法施行法" is "The Enforcement Act of Act of Military Service System", not "Conscription Law".)
A draftee-to-be in the status of an Overseas Chinese having previously established household registration in the Republic of China shall be subject to conscription enlistment according to law upon expiry of one-year period beginning the day next to his return to the Republic of China.
A draftee-to-be in the status of an Overseas Chinese having not established household registration in the Republic of China previously shall be subject to conscription enlistment according to law upon expiry of one-year period beginning the day next to his initial household registration following his return to the Republic of China.
And it goes on and on. The fact that it says "Overseas Chinese" and not "ROC national" seems to suggest Wilz may be included. However, if we look Art. 23 of the parent law, we find this:
Conscription Regulations for Naturalized Aliens and Returning Overseas Chinese in accordance with Subparagraph 5 to Subparagraph 7 of Articles 36 of the Act of Military Service System shall be enacted by the Executive Yuan.
Which points to this:
Recruiting Age Male who has one of the following situation should go through Recruitment re-processing;Those have not gone through recruitment processes should go through the processes and be recruited aster passing:
5- Became a citizen of the Republic of China.
6- Migrated to a foreign country before the Recruiting Age and had returned and reside in the country;The same for those who have obtained foreign citizenships.
7- Studying abroad before the Recruiting Age and had returned to the country after graduating;The same for those who have obtained foreign citizenships.
This seems to say they only care about Overseas Chinese who are also ROC nationals. So, when is an Overseas Chinese not an ROC national?
Overseas Chinese Identity Certification Act
This Act applies to Republic of China ("ROC") nationals who reside in a foreign country, provided that it does not apply to persons with Mainland China, Hong Kong or Macau residency status, or persons holding passports issued by Mainland China region.
So presumably, if Wilz has been certified as an Overseas Chinese through this law, he's an ROC national (which should be clear from the Nationality Act anyway, I suppose). But then again:
Regulations Regarding Study and Counseling Assistance for Overseas Chinese Students in Taiwan
Art. 2 Par. 1 and 2
In these Regulations, the term "overseas Chinese student" refers to a student of Chinese descent who has come to Taiwan to study, who was born and lived overseas until the present time, or who has been living overseas for six or more consecutive years in the immediate past and obtained permanent or long-term residency status overseas. Please note that a minimum of eight consecutive years of overseas residency is required if the person is applying to study in a university department of medicine, dentistry, or Chinese medicine in Taiwan.
A person’s overseas Chinese student status must be validated by the Overseas Compatriots Affairs Commission (OCAC).
And this regulation's parent laws are various education laws, not the Nationality Act or anything to do with the military.
So, since he said he's an Overseas Chinese coming to Taiwan to study, he was presumably certified through the education regulation, and he says he's not an ROC national (although in that case he's actually not an "Overseas Chinese/華僑" as defined in the Overseas Chinese Identity Certification Act), so it looks like he should be in the same category as any foreigner for military purposes.
Still, Wilz should check the Nationality Act carefully (sometimes people just don't realize they're citizens, they don't know everything about their parents and so on) and ask the MND just in case.
Chinese descent = 華裔
Overseas Chinese student = 僑生