Question: What are the spiritual benefits of having only one (or two) meals a day (as in practice of the Eight Precepts)?
Answer: Having one near-noon meal a day (or with breakfast) helps to regularly train in curbing thinking about, and craving for food, which is one of the Five Desires (for wealth, sex, fame, food and sleep). All these falls under the first poison of greed, that bind us to rebirth. When the Five Desires are weakened, it is easier to be free from samsaric rebirth. Lessening eating also trains us to utilise limited energy garnered for other more meaningful spiritual practices.
Question: If a non-Buddhist also has one meal a day, will this person also benefit spiritually unknowingly?
Answer: This would depend on the motivation of doing so. For example, if it is simply due to poverty or miserliness, while craving for food most of the time, there is no spiritual benefit. If the motivation is as above, to train for spiritual purification, yes, there is benefit — of lessening greed. However, if fasting is not done with very clear direction, it might not lead all the way to liberation from rebirth, as liberation requires eradication of all Three Poisons of greed, hatred and delusion.
Please Be Mindful Of Your Speech, Namo Amituofo!