Yes, I did know that the word trundle made sense, because I have come across it before in books, as a kid, in stories for children. E.g. "The gardener trundled his wheelbarrow along the (garden) path."
(The word is not use much nowadays; archaic, as the dictionary entry says.)
I was only speculating about the connection between the two words (trundle and treadmill), because they sound vaguely similar. Maybe they have a common Latin or Old English or Old German root, as many English words do.
Update: I checked, and it seems I may have been partly / loosely correct about the etymological connection:
from trundle small wheel, alteration of earlier trendle, from Middle English, circle, ring, wheel, from Old English trendel; akin to Old English trendan to revolve
This sounds more like convergent evolution rather than a shared root.
Tread derives from Middle English treden; the difference here is to step vs to roll. The latter definition you cite is a newer usage (from the 20th century) which is more directly analogous to the tread on the bottom of one's shoe.
The use of a wheel in a treadmill seems more like an implementation detail; the obvious tie-in (IMO) is "persons treading on steps".
(The word is not use much nowadays; archaic, as the dictionary entry says.)
I was only speculating about the connection between the two words (trundle and treadmill), because they sound vaguely similar. Maybe they have a common Latin or Old English or Old German root, as many English words do.
Update: I checked, and it seems I may have been partly / loosely correct about the etymological connection:
https://www.merriam-webster.com/dictionary/trundle
Etymology
Noun and Verb
from trundle small wheel, alteration of earlier trendle, from Middle English, circle, ring, wheel, from Old English trendel; akin to Old English trendan to revolve
https://www.merriam-webster.com/dictionary/treadmill
c : a mill worked by persons treading on steps on the periphery of a wide wheel having a horizontal axis
https://www.merriam-webster.com/dictionary/tread
tread 2 of 2 noun 1 a(1) : the part of a wheel or tire that makes contact with a road or rail
Italics mine.