Free speech is not freedom from consequence. Therefore, under free speech someone can say something transphobic, the consequence of that can then be they are called out/disciplined for their transphobia.
.Organisations all have policies which tend to include things against discrimination, and in support of minority groups and women. This includes universities and their university student unions. It wouldn't be considered against free speech for an organisation to not employ or to fire someone who was racist or sexist o homophobic, but it is often considered up for debate when someone is transphobic.
I don't know the context from the article that the video was played in, but it doesn't seem it was played in a way that put the safety of trans people first and foremost, especially trans people both who could have been in the lecture aswell as those attending that university in general. As such the person who played the video likely did break university (and union) policies of inclusion and against transphobia. As such it's not denying her her freedom of speech to play the video, but merely saying "You chose to do this knowing it was against our policies, now it's only reasonable you face the consequences". That isn't denying freedom of speech, that is merely upholding the contract between the university and their staff.