Bürgerort (often called Heimatort) is the place of citizenship. Christopher linked to a helpful article about this topic. The Swiss place of citizenship was inherited from the father, so it's both the child's and the parents' place of citizenship. What this means is that Ganterswil (Ganterschwil) and the place of residence would track their baptism, marriage, and burial information. Since the parents' residence is Oberdorf, the child was born in Oberdorf. But both the parish in charge of the residence (i.e., parish of Degersheim) and the parish in charge of the place of citizenship (i.e., parish of Ganterschwil) would've recorded this and subsequent family events. The 1900 baptism record from Ganterschwil isn't available online yet, though; see https://www.familysearch.org/en/wiki/Ganterschwil_Parish,_Sankt_Gallen,_Switzerland_Genealogy (unless you can view the digitized images at this page? https://www.familysearch.org/search/catalog/293775?availability=Family%20History%20Library)

Stellvertreter means proxy, so the baptismal witness column could list someone who stood in as proxy for the actual godparent (though this would be indicated).

Bertha Lienhard is of Sennruthi (Sennrüti, within the same parish of Degersheim).

The child was born on the 17th at "1/2 8 mg [Morgens]"--i.e., 7:30 a.m.