A few thoughts concerning that "anti-dialectics" website:
Firstly the site is trying to grapple with why socialist governments based on Marxism have not succeeded. I think a more usefull and fruitfull starting point would have been to undertake a critique of Leninist organisational methods.
The following are some responces from the author of "dialectics for kids" website:
Einstein said that even one experiment that was counter to his theory would prove him wrong, so it should not take thousands of words to counter Engels--just a few examples, or even one good one. [Rosa Lichtenstein] contends that Engels is wrong in arguing that all change requires "the addition or substration of energy or motion". Rather than denounce that claim, it would be a simple matter to provide some examples of change that do not require addition or subtraction of energy or motion.
The site mentions that dialectial materialism somehow supports the concrete and ignores the abstract. To me this is the opposite of dialectical thinking--i.e. seeing only one side of a contradiction rather than both concrete and abstract, theory and practice, general and particular, etc. So it may be that the site is attacking a straw man.
I notice that the anti-dialectics site takes issue with the catastrophic view of paleontology. It was the fashion for many years in paleontology to believe that change happened gradually rather than in qualitative leaps. This belief was overturned when it was recognized that the impact of an asteroid near Yucatan about 65 million years ago undoubtedly led to global cooling and the sudden demise of the dinosaurs. The anti-dialectics site is still arguing that the extinction of the dinosaurs occurred over tens of thousands of years and was not a relatively sudden event. I think this is counter to all the scientific evidence.
Another thought I had is that this is not just a matter of academic debate. Right now the concentration of carbon dioxide in the atmosphere is about 380 parts per million, having risen from the pre-industrial level of about 260 ppm. Nearly all scientists agree that there will be a point where the concentration of carbon dioxide is sufficient to cause enough global warming to melt the polar ice caps. The book Hell and High Water estimates that the turning point could be around 460 ppm, whch gives us about 20 years to stop the increase in carbon dioxide before it is too late. Failing to recognize that there are qualitative turning points in all of nature is a serious matter which could lead humanity to disaster.
[The site claims that gravity is not dialectical, however: ]
Gravity is always experienced as the attraction between two objects and there are always countervailing forces--the molten core of the earth resists further collapse by gravity, the nuclear furnace at the core of the sun resists collapse, the motion of the moon keeps it from falling to earth, etc. Each of the four fundamental forces--weak and strong nuclear forces, electromagnetic, and gravity--act through the exchange of particles--photons in the case of electromagnetic forces, and gravitons in the case of gravity. So all of that seem pretty dialectic. The tricky part is that gravity distorts space and time, which gets into black holes and the general theory of relativity. I love thinking about all that, but I do not pretend to fully understand it.
But not having a complete understanding of something is not the same as agreeing that it is not dialectical. I don't see any reason to draw that conclusion.