How come mere water buffalo milk and lemon juice mixture turn into yogurt? Yogurt is produced by the fermentation of lactose in milk by the bacteria of yogurt-ferment. Without those bacteria it is not possible to make yogurt.

But surprisingly, water buffalo milk and lemon juice mixture turns into yogurt without any third ingredient. You may first boil the milk to sterilize it; the result doesn't change. The milk must be water buffalo milk, cow milk or another animal's milk doesn't make yogurt this way. One of my relatives made yogurt this way, so this is not a myth (if you didn't hear this before). Unfortunately I couldn't find an English recipe to share with you here.

Can you please explain to me this chemical phenomenon? Is fermentation involved in this process? Is this resulting "yogurt" actually a yogurt by definition in the perspective of cooking and chemistry?
This is not yogurt per definition, you are making a fresh cheese. You can actually use other types of milk for such a cheese, but the mouthfeel and taste will be very different and won't be as similar to yogurt. 

There is a large class of acid-curdled cheeses, including paneer, tvorog, quark and many others. I don't know if yours has a specific name. I know that there are people who for some reason can't tell the difference in taste betwen quark and yogurt. But it is still cheese, even if it tastes similar to yogurt.