Being Chinese-American, I grew up on this stuff. The English name "Chinese steamed eggs" comes from the fact that it comes from Chinese cuisine, and that "steamed" comes from the word 蒸 in 蒸鸡蛋. The word 鸡蛋 refers to "chicken eggs", but the word 鸡 may refer to chicken or turkey. The word 蛋 refers to "eggs". The Chinese language has no singular/plural distinction, but contextually, we know it's eggs, not an egg, because we often use two or more eggs.
During the food prep, the eggs must be beaten. Afterwards, some water is added to increase volume. Salt may be added for flavor. Then, the eggs are set in the steamer to be steamed.
In Chinese cuisine, there is also a separate dish called 番茄炒鸡蛋, which involves tomatoes and scrambled eggs. 炒 refers to a cooking process. The Chinese definition of this cooking process is: "把东西放在锅里搅拌着弄熟". Basically, you put something in the wok and mix until ready or fully cooked. Often in Chinese-American restaurants, 炒 may refer to the process of stir-frying. In this dish, 番茄炒鸡蛋, the eggs are stir-fried, but I think the process and the finished result look indistinguishable from scrambled eggs. I mean, you really do scramble the eggs, dump the eggs in the wok, and then stir-fry the eggs until fully cooked.
Here's the tricky thing. The English word "scramble" seems to refer to the process of beating the eggs. If that is the case, then wouldn't Chinese steamed eggs be considered and classified as a form of "scrambled eggs"? Or should Chinese steamed eggs be considered/classified as "steamed eggs"? Or should this recipe fall under both categories - "steamed" and "scrambled"?