Apparently after the battle Sir Robert Babthorpe complied a complete list of every man present. If that included the infantry, it must have been a very long and pointless list, but maybe the infantry didn't count as men but were considered a lower form of life.
The list is mostly lost, though Joseph Hunter is said to have found some fragments in the 1850s.
But Ralph Brooke had access to the list in 1604 and made an extract, which survives in 3 copies - Bodleian, College of Arms, and Harleian (British Museum).
The Nicholas Harris Nicholas book is based on the Ralph Brooke extract.
The list in the book was republished in the Family Chronicle magazine in 1997, and online by Kenneth Fitton to the soc.gen.medieval newsgroup in 1998. Other sites have taken it from the book or the newsgroup. I don't know if Fitton got it from the magazine or direct from the book. You can recognize this version by the unlikely "Conrad Aske", 8th from the top, where the book has the original "Conand Aske".
Brooke didn't copy the complete list of names. The infantry are ignored completely, but it's hard to know what else got lost or corrupted. Apparently one would normally expect heavy cavalry, who were all knights and squires in full armour, and light cavalry, so it's not clear who is included under Lancers. Monsr indicates a knight, but the puzzle is to know whether all the other names can be taken as squires.
Even if they can, the names are hard to identify positively, because anybody of any prominence is likely to have had some obscure namesake lording it over some one-horse manor somewhere.
The much shorter list on Genealogics presumably sticks to people who are positively identified, mostly knights.
Another question is whether Brooke kept the spellings as he found them or modernised them to those of his own day. Actually it's not entirely clear that the original was in English.