Techniques for enhancing the amount of 'background blur' do exist (not 'bokeh' per se). One demonstration says, " If you don’t have a nice DSLR camera, or you have an existing photography that you want to add production value, this tutorial will show you how to achieve this soft/out of focus effect in photoshop." It first requires that you cut out the subject, then apply a Blur Gallery tool. Of course, it's not quite as simple as that, as there are some subtle techniques that are also applied
The linked website of OP uses a 'green screen' technique to isolate the subjects during shooting, and then puts the subjects onto a variety of artificially added backgrounds during postprocessing. There are some with superimposed foreground elements as well, and I do not know how those are achieved.
And, as one reply infers, 'good lighting' has to be employed to illuminate the green screen as uniformly as possible, and have NO SHADOWS from the subjects fall upon the green screen!