Afaict this is caused by the ancient 1.8.9 LiteLoader shipping with an equally ancient Mixin lib (version 0.5.3) that is too old to work with the ReplayMod.
ReplayMod ships with its own version of the Mixin lib but that's not getting used because LiteLoader is being loaded first.
Once way to work around that is to install LiteLoader as a Forge mod as described here.
There is nothing we could change in the ReplayMod to automatically fix the problem, so above workaround will be required until LiteLoader releases an updated 1.8.9 version (which is probably never going to happen).