I got this plugin working in 2.9.1, but I did the following:
1. On lines 200 & 202 "sponsors-slideshow" was misspelled as "sponsors-slieshow". So, I corrected that.
2. On the Links/Posts new pulldown menu the links category automatically defaults to your default links category; BUT, it doesn't show the option to change it to another links category. After messing around with it, I figured out that if I changed the drop down to 'Posts' and then back to 'Links', I could make the 'Link Category' option appear. Interestingly, once i saved my choice, it no longer showed the option within the widget edit box, however it did update the options and now it works.