Other than cattlemen's cattle, what species do wild horses and burros displace?
Here is one definition of "invasive species."
As per Executive Order 13112 an "invasive species" is defined as a species that is:
1) non-native (or alien) to the ecosystem under consideration and
2) whose introduction causes or is likely to cause economic or environmental harm or harm to human health.
The feral horses and burros would displace native ruminants: bison, deer, elk, caribou, etc. etc.
The link I posted has a list of quite a few invasive species, but it is not inclusive.