Question: Are those little bags of chai you dip into hot water actually Chai?
Short Answer: It depends on how you look at the question but the Chai For blog has the complete answer for you.
The shortest answer is... kind of. It depends on if you're looking for a traditional chai or not. Let's dive in.
To determine if those "tea bags" constitute is Chai is to understand that the question's answer is partly linguistic. This means the answer somewhat depends on how the word is being used. Many languages of the world speak the word "chai" to simply - and generically - mean "tea." In that sense, then yes this is technically a form of chai if "chai" means tea.
But who are we kidding? Offerings from various companies claim this "tea bag" is chai simply because it has a technically correct blend of the tea and spices that make a traditional cup of chai.
However, "technically" containing these ingredients does not mean it is an authentic chai in the terms we are speaking: you know, a traditional cup wit all-natural ingredients such as cardamom, cinnamon, ginger, cloves, and black pepper. The kind of chai that is brewed with milk and sweetened to taste, creating a flavorful and aromatic beverage.
Authentic chai is made with a very specific black tea - most typically Assam or Darjeeling - and is grown in the states of Assam or Darjeeling, India. This is a specific tea blend with a specific flavor (oh, and is the exact set of ingredients we use to make our chai blends!). Further, it's not just "having" the right spices - but making the right proportion - that create that dynamic, timeless, authentic flavor.
Furthermore, a truly authentic chai is never just going to be steeped directly in water alone. In India, the most traditional blends could be 50% water and 50% milk - or even 100% milk but it is never 100% water. The provided directions to brew our chai mirror that tradition to help you easily achieve a traditional cup of chai that is brewed in both water and milk.
But it's not just the ingredients - its also how the ingredients are actually prepared that make a great chai. With these tea bags, the English (or American, or "Western") style of preparation is to set the tea bag directly inside pre-heated water and wait for it to infuse. The magic of a truly great cup of traditional chai is that the water and the milk are very hot - still simmering or even boiling, while simultaneously activating the tea and spice blend to infuse into a warming cup of delicious chai.
Check out the color differences between chai steeped in just water and chai steeped in milk and water. 
Let's hammer this home with a comparison. It's like making authentic tacos. There are thousands of people who buy a shredded cheese blend, add a packet of unseasoned beef, and put it into a hyper-processed "corn" ("airquotes") hard tortilla shell and it might visually resemble a taco, it might vaguely taste like a taco, but it is not at all true to what makes an authentic taco. That is what tea bags of chai are.
The Bottom Line: Traditional chai is real tea, real spices, brewed together in high heat with a mixture of water and milk (or entirely milk!). So, Chai "tea bags" aren't really traditional chai - even when they might have the correct ingredients.
