I'm sure we've all vented about some topic where we've made a generalised comment about a group, place, institution etc. based on a specific instance or string of events - that's just one of the ways frustrated expression has developed. Taking a very benign example, if you have a bad journey to work for example:
"Ugh, I strawberry floating hate trains, why are they always bloody late!"
Is every train late - no of course not, but it may feel that way sometimes! If it helps you vent some steam, and potentially get some sympathy from others - "sorry you had a bad journey Tony, trains can be annoying!
"
Does anyone in that situation really believe trains are gooseberry fool to their core and that every train is out to get them? No of course not, that would be ridiculous. I don't think it hurts to apply the same standard to most expressions like those being discussed here - for the vast majority of the time people are just venting and not trying to take part in some widespread conspiracy to seed the notion that some sub-group of individuals are inherently evil!
EDIT: Also I have to admit I dived into this conversation mid-way through and never addressed the origin - it's clearly strawberry floated up that Razer took this stance to a streamer responding to harassment in this way!