Assume the animals are extinct due to hunting or just climate change. Perhaps humans got good at hunting a little too soon in this TL and wiped out the megafauna in the Old World as well as the New, before anything could be domesticated. Goats, sheep, pigs, alpacas, turkeys, dogs and chickens are exempted, as they can't really be used as draught animals too well anyway. But no camels, donkeys, horses, cows, or even llamas (though they aren't that large really). Let's also assume elephants are extinct as well, though other large non-domesticable animals are left intact.
I think the Inca scenario is a good observation, as they are an example of such a civilization that has no good draught animals. The Aztec and Maya are as well. So we'd probably be somewhere in the bronze age, (The Inca had bronze at least, and some Mexican tribes supposedly were attempting to use it when the Europeans arrived.) with an alphabet, probably paper or some substitute, decent agriculture, a good calendar, etc. But civilization would probably be well behind OTL.
Would they eventually modernize (think into the future here, even millenia if necessary)?
I can't picture these people coming up with railroads and cars, at least not very quickly, possibly not ever. What would they have had to build off of?
However, they might surprise us. I'd guess canals would become a major mode of transportation, eventually much more widespread than OTL. And what about air travel? Without a major road network from prior horse-drawn vehicles, perhaps instead of highways, they'd use the water as much as possible for heavy loads, and airships or planes for passengers? (thinking well into the future here)