First, let us pretend for a moment that the sentence is:
Do you feel comfortable with this sentence? It means:
"If one did this, this anime would survive for the next 100 years."
What to do to make it survive a long time must have already been discussed in the conversation, mustn't it? That is why you can say 「こうしたら」.
This is all about the famous こそあど. If you have a word starting with こ、そ or あ, then a "what", "how", "where", etc. has already been mentioned or discussed in concrete terms in the conversation. If it has not yet been discussed, and you want to talk about it, that is when you use a どｰword. So, you have a 「どう」 this time.
Back to the original sentence..
「どうしたら」 is, of course, a conditional phrase, which is actually difficult to translate by itself. It literally means "If one did what". The sentence is talking about "what to do" or "what should one do" to make the anime last long. Are you following?
「どうしたら」 modifies 「残っていく」. ← Important "what to do (so that) it will survive"
"I can't understand what 'how' is referring to here."
This statement worries me somewhat. Forget "how"; That is just your literal translation of 「どう」. Instead, you would need to get used to the highly common collocation of 「どう + する」 to mean "do what", "what to do", etc.
「どうしよう！」= "What should I do?"
「どうしたの？」 = "What happened?"
Those phrases should sound familiar to anyone who has been studying Japanese over 6 months or so.
The reason that the sentence in question seems difficult to comprehend, according to me, is the fact that it has not only a very long object but the object contains within itself a mini-sentence consisting of a condition and consequence. The object of the sentence is:
That is what the speaker/author wants you to think about。
「(Object) + （を） + 考えてほしいと思います。」
「を」 is not used, but it can be.
"I would like you to think about (what should be done/what you should do/what to do) so that this anime continues to survive the next 100 years."