Good meme but the fact is that ice cubes don't contain very much water, you're unlikely to eat enough ice in a day to stay hydrated. An average ice cube contains about 2 tablespoons of water; 1 cup of crushed ice equals just 1/2 cup of water, according to The Ohio State University Wexner Medical Center. So it is 50% water.
If an average American needs to drink about 0.84 gallons (3.19 litres), that would mean you require about 14lb of ice (6.4kg).
So technically it is water that you can eat but it won't help you hydrate.