The Cape York Peninsula Land Use Strategy website is from 1995, which is a bit older than some other resources, but there is yet to be an updated version of this. The website does a great job at setting the scene in terms of thematic areas regarding land use on Cape York. However, as you rightly pointed out, some of this information may be outdated so it is important to supplement with your own research. We have some more recent resources which can help you with this, such as Queensland Government, Parks and Forests ‘Aboriginal freehold land and jointly managed parks on Cape York Peninsula’, which can be found in the Thinking About Indigenous Homelands and the Cape York Peninsula page.
To answer your question specifically, weeds and feral animals do still remain a threat to the environment in Cape York. There are some resources under Design Area 1: Transport and Access which give some more insight into this, as well as wider research you conduct.
Hope this helps!