Upvote:4
VietJet is a LCC (Low cost carrier) and like most LCCs is a point to point carrier. You check in for A to B, then at B claim your bags and check in for B to C.
For domestic to domestic flights this is not a big deal, but for international to international it does mean clearing immigration and customs, to claim and recheck your bags.
But sadly as has been mentioned in numerous similar questions, it is the traveler's responsibility to make sure they have the correct documents for the trip they are undertaking, which includes any transit points. Kayak is not responsible for telling you, nor is VietJet. The airlines only responsibility is to the government of the destination to make sure a traveler does have the necessary documents before boarding them and denying them if they don't (as in your case).
You can try filing a complaint with your credit card company, but they will likely side with the airline, as they understand where the responsibility lies.