This is just an educated guess that I've never tested or seen specifically tested with lenses that have been highly corrected for field curvature and astigmatism, which are intimately related.
Most lenses highly corrected for field curvature are used for macro work or to do reproduction of flat two-dimensional documents/artwork (or to score very well on shooting flat test charts at close distances so the seller can declare they have the "sharpest lens in its class"). In such cases, the aesthetic properties of the background blur is not a primary consideration when designing the lens.
Lenses with uncorrected or undercorrected field curvature often also demonstrate sagittal astigmatism. The two things combined, especially when used on a moderately wide lens with a very large aperture that results in mechanical vignetting, can produce a "swirly" type of bokeh often called the "Petzval effect."
Most lenses that give such "swirly bokeh" involve a form of mechanical vignetting.
The wide open aperture on the left demonstrates mechanical vignetting, when all of the entrance pupil is not visible due to the barrel of the lens blocking part of it from an area still within the lens' field of view. Even without any appreciable amount of field curvature or astigmatism, such a lens will demonstrate "cat's eye" bokeh.
Add uncorrected field curvature to the equation, as well as a scene with lots of bright out of focus highlights, such as a bright sky behind foliage, and one gets the "swirly bokeh" effect.
What swirly bokeh technique is this and how can I achieve it?
What is the cause of this non-uniform bokeh effect?
If, on the other hand, the lens is highly corrected for field curvature to give it a more or less flat field of focus¹ and the lens also demonstrates tangential astigmatism, it seems to me the shape of the bokeh would be stretched in a radial direction from the center of the lens such as demonstrated in the example photo included in the question. By strongly correcting for field curvature, the astigmatism can shift from sagittal (as when FC is not corrected) to tangential. If sagittal MTF is higher than tangential MTF, then tangential lines will be blurrier than sagittal lines, thus spread out over a larger area in the direction perpendicular to those tangential lines.
What most of us consider "good" bokeh, in terms of the quality of the out-of-focus highlights, results from lens design that leaves field curvature and/or spherical aberration undercorrected or uncorrected. That means such a lens won't be the best candidate for other types of photography, such as landscape or architecture, when we want good sharpness all the way to the edge of the frame.
The classic example of this is the Canon EF 85mm f/1.2 L II. What gives it such great bokeh is the uncorrected field curvature it demonstrates. This makes it a totally inappropriate lens for doing flat reproduction work or for shooting flat test charts because the field of focus on the edges and in the corner will be a considerable distance in front of the flat subject when the center of the lens is perfectly focused on it. If you want to shoot a perfect photo of a flat test chart, the $350 EF 85mm f/1.8 absolutely cleans the floor with the $2,000 EF 85mm f/1.2 L II. But when you want that mesmerizing bokeh on the edges of a portrait there's nothing like the 85/1.2!
¹ Keep in mind that most lenses demonstrate some field curvature. The field of focus is not a perfectly flat plane, even with a theoretically perfectly manufactured lens. Lenses that are highly corrected for field curvature, such as many macro lenses, still have a field of focus that looks more like a lasagna noodle than a flat plane. They're not perfectly flat, they're just more flat than uncorrected or less corrected lenses. For more about the subtleties of field of focus, I recommend reading Roger Cicala's excellent series about it:
Fun with Field of Focus Part 1
Fun with Field of Focus II: Copy-to-Copy Variation and Lens Testing