Well I guess I will start by saying that MHD is a much broader field than just this paper. This is detailing a method of generating power from an ionized gas (plasma) moving through a magnetic field, but MHD covers the flow of any fluid under the influence of a magnetic field for many, many purposes.
Anyway, moving on, nothing in here makes me think that this is no longer a popular idea. The study started in 2001 and was published in 2007. That is very recent. Why do you say it is no longer popular?
The reason you haven't seen it on a plane or other vehicle yet is because there are no hypersonic vehicles at this point in time, and that is the only way this concept works. It needs a scramjet, and it was only recently shown that a scramjet would work the way it should. A ramjet wouldn't get the internal flow fast enough to see dissociation of the gas. Still, there are several more pressing issues to tackle when it comes to getting a hypersonic vehicle flying, most notably perfecting the scramjet, understanding boundary layer stability at those speeds and developing materials that are lightweight and strong while also being resistant to extreme heat. They all must be understood better before an MHD power generator would be feasible.
Obviously you need a working scramjet for this system to work. The problem is, this system was studied in an idealized case where the flow was passing through the annular channel between two cylinders. Scramjets aren't build that way. Scramjets must be built in very precise ways in order to get them to start, otherwise you just end up with a fast-moving, inert hunk of steel and metal with no working engine. Something would have to be reconciled between the current working designs of scramjets and the studies on MHD power generation.
In addition to the shape, the engine requires an additive seed chemical to get it to burn hot enough to ionize the gas. Ordinarily, a scramjet would not get hot enough. This means that you need a material at the scramjet nozzle that is even more heat resistant than you would have otherwise as well as more heat resistant materials inside the combustion chamber. Both of those are limitations that likely cannot be solved yet without considerable research.
Additionally, you would have to get those seed particles to mix into the flow, which is not very easy to do. They have problems right now trying to get the fuel to mix in with the flow, as the incoming air flow is naturally laminar. The solution is to trip the flow heading towards the inlet which is done using huge trips since we don't completely understand the transition process at those speeds. Then you combine that with essentially a fuel injecting mesh that injects fuel into all points of the flow instead of just the wall or a single point. Now you have to add another mesh for the seed particles, which is more blockage and diminished power.
The final problem is that in extracting energy from the flow, you are slowing it down and losing thrust. Current scramjets such as the X-51 can only just keep the vehicle moving at the speed the rocket leaves it. They can't push it any faster yet. Basically, that means that taking any thrust out would mean they can't even keep the speed constant where the rocket leaves off.
What does all this mean? It means we are years away from seeing this kind of technology on a hypersonic vehicle because there is just so much to do to even make a working vehicle still. Once that happens, then someone can see if an MHD generator is even feasible on a real hypersonic vehicle rather than just in a lab.