Well, I guess it is all open to interpretation on what constitutes a "great cavalry charge". I don't believe there is an instance of four of five thousand cavalry all lined up en masse for a charge since the Napoleonic Wars, but if you want to waste your cavalry like this in F14 then you have the right to do so! Who knows, maybe you can find a situation where that might actually accomplish something if the enemy helps you out of course.
All that aside, sure - as a generic answer in general terms, there were plenty of cavalry charges in 1914 and World War One in general, but they would be considered individual actions -- except on the East Front where there were countless swirling cavalry battles since the cavalry was free to roam and maneuver to its fullest potential (because of the open space to pursue / outflank and even raid rear areas). In the west, there is the famous German cavalry charge at Haelen against dismounted Belgian cavalry which was very bloodily repulsed, and the British cavalry charged at Elouges with two full regiments (~1000 men) only a day after Mons to by some time for the rest of the BEF to withdraw. In the case of the latter the British got (in game terms) disrupted in the attempt and shot down in large numbers before they broke off). That website that says that the last cavalry charge on the Western Front occurred at Mons (I assume they are talking about Elouges), is quite a generic and incorrect statement. There were so many actions by all forces involved from August to the Marne, and from the Aisne to the English Channel (Race to the Sea) and a lot of those actions are undocumented and were of course chaotic to say the least. There was a cavalry action around Villers-Cotterets just prior to the 1st Battle of the Marne where the German 4.Kavalerie-Division was almost wiped out completely, and those are just naming a few documented events off the top of my head.
Once the front line settled down after the Race to the Sea, cavalry pretty much became infantry with fancy uniforms and traditions to occupy trenches like everyone else, or they were held back in reserve as a breakthrough force (think of Cambrai 1917). But after 1914 in the West Front, it would be true (for the most part) to say that cavalry played a big role only on the East Front and in the Near East Front after this point, and it would also be true to say that World War One was the twilight period of *traditional* cavalry.