Answer: Fasciolopsis buski, the intestinal fluke.
The first step in making the diagnosis is recognizing that these objects are flukes - flat 'leaf-like' worms (member of the Platyhelminths) with an oral and ventral sucker as shown below. The oral sucker isn't fully demonstrated in the photo.
The size of the fluke is also important. As Lukus points out, the flukes that were obtained at microscopy are on the small side for F. buski (2 to 3.5 cm in length), but mature forms are larger (up to 7.5 cm!). I believe we can see some larger flukes in the endoscopic video.
Hans points out that there are also other intestinal flukes such as Metagonimus yokogawai and Heterophyes heterophyes to consider, but that they are much smaller in size and wouldn't be in the differential in this case. Also, the larger thin-walled, operculated eggs (without a shouldered operculum) fits nicely with F. buski.
Of note, edema is a common presentation in individuals with heavy infection, as seen in this case. Other manifestations include diarrhea, fever, abdominal pain, and intestinal obstruction.