the current way:

(initial dialog for a "rescue pet" quest encounter)

One of the cavemen here is offering a reward for rescuing their kidnapped dog.

Do you want to go for the reward?

Yes

No

the "caveman-speak" way:

ugh!

bad people take dog!

me miss dog!

me no hunter!

me no warrior!

you get dog!

bring dog me!

me give reward!

we deal yes?

This seems more like a "text prompt or dialogue" question to me. With that it depends on if you want quick 'chat' times, or higher immersion. If immersion is your goal, I'd definitely go for the caveman talk.

The second is funnier, but I could see it wearing thin after a while, since your whole game is interacting with primitive people.

"Caveman speak" is bad linguistics. Don't do it unless you're going for a cartoony or comedic approach.

Actually, it would probably get really grating over the length of an entire game, so even if you ARE going for cartoony or comedic, you should probably tone it down a little.

I'd say definitely no. Simple language would probably be good, but caveman speak is not.

Perhaps you can have both clear writing and the "feeling" of a lack of sophistication, by having regular writing with a special font and perhaps all lowercase sentences.

Fonts and use of uppercase/lowercase can convey character. One example is Death from the Discworld series of books, who had a special font and all-caps writing for his speach.

The trouble with "caveman talk" is that it makes everyone who speaks that way sound like an idiot, and it'd be very annoying to spend 50+ hours talking solely to idiots. (Nor is it especially realistic.)

If you're going for a "dawn of language" feel, it might be better to write in a way that's mostly grammatically fluent but with a very restricted vocabulary (like "Green Eggs and Ham" or "Up Goer Five"), and maybe with some syntactic restrictions (like no embedded clauses and/or only present-tense sentences). A reader can rapidly become accustomed to restricted-vocabulary text in such a way that it doesn't grate, but it still affects the overall feel of the text even after readers stop noticing it.

Moving this to Writing. I think caveman talk can work, if you apply it consistently and with humor.

Maybe hybrid:

One of the cavemen here looks distraught, when you approach he tells you

"ugh! Bad people take dog! You get dog! Me give reward!"

Will you agree to find the dog?

Yes

No

I think it could work too, but you're going to have to be wary of it wearing thin as other's have suggested. I second the idea of accomplishing this by developing a restricted grammar productions and word list -- don't just start with full and arbitrary modern dialog and then caveman-iffy it.

I'd maybe look at how much vocabulary Coco (the Guerrilla who was taught to speak sign-language) had, and how well she formed sentences. Its hardly scientific, but at least its some kind of modern analog.

I'd half-jokingly suggest considering a pictographic language based on cave-paintings (There actually are real-life recurring cave symbols that some scientists believe are a pictograph language of sorts) -- its probably too high a barrier to entry to work for real, but thinking about dialog in those terms might help. If you did actually do a pictographic language in the game, it might be an interesting mechanic in itself, but I think you'd have to ramp it up pretty slowly -- very short clauses made of the most obvious symbols -- so that the player could build up to more complex thoughts and abstract symbols, but learning to decipher things could be part of the fun.