Yes, it’s keeps, as you have reasoned in the question.
Your source is not correct:
In history class
yesterday today, I got 'm getting mad. The videotape we were are watching irritated irritates me because the narrator kept keep trying to force his opinion down our throats . . .
I'm tempted to believe this is a simple typographical error where a single letter has been mistakenly omitted. It may not be deliberate.
To use keep might be held to be correct if the sentence were in what is commonly called the “subjunctive mood”:
If the narrator keep doing that, I shall get mad
...but that is so archaic and awkward that it is almost perverse. To use “If he were to keep doing that” is not much better, and even there If he keeps is to be preferred.