The question why is that throw called Polish is indeed interesting. I would also like to notice that "Polish" could also meant Lithuanian, Belarusian or Ukrainian. Because it was not uncommon many decades ago to call people of these nationalities "Polish" in the West due to Polish-Lithuanian Commonwelth and Second Polish Republic borders. At least Ukrainians of these three were also practicing (and are currently) folk wrestling forms with rules and grips like in Biady.
BTW Do you maybe have idea why is "Belgian takedown" called the way it is?
As for the name "Biady" I guess that it's not the only name that was in use in Poland for various folk wrestling forms. I would like to bring to your attention that there were various "zabawy z mocowaniem" present in the past. Some of them would be familiar to many people of millenials generation and had a somewhat abstract rules. Sometimes it's hard to say were they longer existing traditions or spontaneous creations emerging independently in many places around similar time because of simplicity of main concept behind them. As for older people (generation of these typically in their 80s and 90s now) from what I know from stories I heard not all of them were associating their (various) games of "mocowanie się"/"siłowanie się"/"przepychanie się"/"przewracanie się" with wrestling. Some of them did, other just were insisting that it was only "childish games" and not wrestling at all.
There been some attempts to start discussion on general topic of martial arts related games and folk style sport traditions of Poland and neighbor region back in the mid '00s but Polish historical reenactment crowd at the time preferred to laugh at idea of such traditions even existing in the first place. Discussions on such subjects typically ended with "śmichy i chichy" instead of serious treatment of the topic. It were strange times where even authenticity of many European martial arts including for example French Savate was questioned (concept of Europeans using kicks in fight was too mind blowing for some people back then, according to them kicking was something that only Asians do, and when they do it's all flying roundkicks despite many sources confirms that use of kicks in Asian martial arts was far from acrobatics of most of 20th century Honk Kong production choreography) and revival of folk wrestling forms in eastern neighbors of Poland was also questioned (without doing any prior research of course) as "modern nationalistic invention that has no any base in historical reality just because I said so do not try to question my wisdom". I'm talking here about Lithuanian and Ukrainian traditional folk wrestling, Ukrainian folk fist fighting, Ukrainian Cossack wrestling etc. Too my knowledge none of these critics ever been to Lithuania or Ukraine back then and ever since then to verify and potentially learn some useful things about ways these traditions get preserved there. And they had almost 20 years to do so.
I'm glad such times are over and Poles started actually researching that topic instead of laughing at it. Too bad amount of living people remembering local wrestling games and traditions drastically decreased in these years that passed since first discussions in reenactment circles.
Was such long delay caused by very typical for generations born during and shortly after end of communism in Poland distaste for anything "ludowe" (very commonly seen by them as "przaśne", "dziadowskie", "prymitywne")? A toll of decades of communist government appropriating everything folk related for goals of regime propaganda resulting in at least two generations being fed up with "folk themes". Or were there also other factors? Political regimes of countries behind so called "Iron curtain" has a long story of suppressing "not sanctioned and controlled by the government" activities even slightly reassembling martial arts. That could explain lack of any publications on Polish folk wrestling during "real socialism" era in Poland. There was analogous situations in other countries of the former soviet bloc and satellite countries where there been pre World War One and World War Two mentions (and sometimes photo and film evidence) of local martial arts and folk wrestling and then silence for several decades during "governance of The Representatives of The People" a.k.a. communist/socialist regimes. And only at the very end of these regimes (in the'80s) or after their fall (in the '90s) we can see these traditions being brought to public attention again. If you wanted to train even more "mainstream" and "fashionable" fighting styles like for example karate in many of these countries you had to belong to certain "organizations" (under strict communist government control) or get special permission during socialism/communism times.
