Dehydrogenation reaction of alkanes is inherently endothermic as one removes two thermodynamically more stable C-H bonds and replaces it with one less stable C=C. Although the product is conjugated with the carbonyl group, this stabilization should be negligible, shouldn't it? How comes then according to the scheme below, the result of this reaction are two high-potential electrons capable of forming ATP from ADP? Is the reaction concerted with some other not shown here? Or is the enzyme regenerated afterwards with some input of energy?
You have to consider the full redox reaction to determine if the reaction is favourable or not. It's not correct to think of enoyl-CoA alone as "higher energy" than acyl-CoA, because of the free energy difference $\Delta G$ of the half-reaction:
acyl-CoA $\leftrightarrow$ enoyl-CoA + 2 $e^-$
cannot be determined without knowing what the electron acceptor is. You might be thinking of the enoyl group as "higher energy" because it is reactive towards H$_2$ (as in hydrogenation reactions), but that's not the relevant redox couple here.
In this case, we should consider the energetics of the entire process of electron transport, as shown in your diagram. Since the intermediates (FAD, ETF, quinones) all cancel out, the overall reaction without ATP synthesis is:
acyl-CoA + 1/2 O$_2$ $\leftrightarrow$ enoyl-CoA + H$_2$O
This reaction is highly favourable, with a $\Delta G$ of about -150 kJ/mol, because O$_2$ is a very good electron acceptor. (See this site for free energy calculations.) This is more than enough to drive ATP synthesis (about 45 kJ/mol).
The reason is that the reaction is not solely a dehydrogenation, but more properly, oxidation of the two central atoms.
In the C-H bond, the C is more electronegative, which means the electrons they share will be more on their side - the carbon is in a reduced state. In the reaction you pointed, it's not only the H+ that leaves, but also one electron per H+ (so that makes one H atom leaving, but since electron was more of the C than the H, it's actually the C that is losing an electron - being oxidated). Those electrons are then stored on an electron carrier (FAD --> FADH2), which goes on to provide those electrons to the electron transport chain in the mitochondria, enabling the production of ATP. (know more about this process: https://en.wikipedia.org/wiki/Oxidative_phosphorylation)