You're comparing disparate things. The paper is investigating the increasing accumulation of deleterious mutations with paternal age at conception. There's no doubt that this happens from what I can see. There's an extensive citation list at the end of the paper. You should take a look at it.
The Hajnal line theory is something completely different. It has to do with the declining fertility in certain parts of Europe through a combination of late marriage and high rates of celibacy particularly for women.
For those unfamiliar with it.
https://en.wikipedia.org/wiki/Hajnal_line
Where did you get your map, by the way? I haven't seen any that have the line that far east. Most of them look like this, with at least half of Poland being east of the line.
A more modern examination of it in a mega data study can be found here:
http://eml.berkeley.edu/~webfac/eich...n/Dennison.pdf
The most persuasive explanation of it I've found is a connection to the manorial system.
I think it's clear how this could be of benefit economically in certain circumstances. I've mentioned quite a few times that I saw the operation of this in real life in my own area. Land, especially fertile land, was scarce, whether you owned your own land or rented it from a landlord. In the latter case, it was a form of sharecropping. Upon the death of the landlord, to whom would the landlord give the lease? Through tradition, it was usually given to the "family", but to which man? Obviously, it would go to the strongest, the most capable and intelligent. Other intelligent siblings might go into the priesthood or the convent and some boys might engage in trading or join the army. The rest stayed as unpaid labor on the farm. Family control was strict. No daughter would be given to a man who didn't have land to farm or a decent job.
What the authors are investigating, as I said, is something completely different. They are investigating, in effect, infant and child mortality based on paternal age.
There are all other kinds of studies based on congenital birth defects by area which I've seen, but paternal age at conception is only one factor; there are all kinds of environmental possibilities as well, including rates of alcoholism, lack of nutrition etc.
"The effects of paternal age on offspring are not yet well understood and are studied far less extensively than the effects of maternal age.
[61] Fathers contribute proportionally more DNA mutations to their offspring via their germ cells than the mother, with the paternal age governing how many mutations are passed on. This is because, as humans age, male germ cells acquire mutations at a much faster rate than female germ cells.
[6][7][22]
Around a 5% increase in the incidence of
ventricular septal defects, atrial septal defects, and
patent ductus arteriosus in offspring has been found to be correlated with advanced paternal age. Advanced paternal age has also been linked to increased risk of
achondroplasia and
Apert syndrome. Offspring born to fathers under the age of 20 show increased risk of being affected by patent ductus arteriosus, ventricular septal defects, and the
tetralogy of Fallot. It is hypothesized that this may be due to environmental exposures or lifestyle choices.
[61]
Research has found that there is a correlation between advanced paternal age and risk of birth defects such as
limb anomalies, syndromes involving multiple systems, and
Down's syndrome.
[6][22][62] Recent studies have concluded that 5-9% of
Down's syndrome cases are due to paternal effects, but these findings are controversial.
[6][19][22][63]
There is concrete evidence that advanced paternal age is associated with the increased likelihood that a mother will suffer from a
miscarriage or that
fetal death will occur.
[6]"
https://en.wikipedia.org/wiki/Congenital_disorder
Map of congenital anomalies per 100,000 in 2004

I think it should also be kept in mind that very young age in the mother, and even in some cases in fathers, has also been shown to have deleterious effects. That may be one factor, in addition to close cousin marriage, for the feebleness of many offspring of aristocratic families, since the girls were often married off very young.
Someone also claims to have found a correlation between mean within country IBD rates and the Hajnal line.
Hajnal line and IBD rates.jpg