The usual justification for your question is that "I am seeing someone" means that you are dating that person. Or that you will see them in the near future (e.g. I'm seeing my favorite band tomorrow). But "sehen" does not have any of those meanings, and so you can't translate with the continuous present in this case.
The same happens with some other verbs:
Ich habe ein Baby: I have a baby. If you say "I'm having a baby", it means that you are pregnant (or your wife is), but that's not what the German sentence means
Ich habe Fleisch: I have meat. If you say "I'm having meat", it means that you're in a restaurant picking your food, not that you have meat (in the fridge, in your body, etc)
Hope it makes some sense...
Now assume that it is the person that sees the animals (and not something else). Would that be “die Tiere sieht die Person”?
(If so, I'll stick to using only plurals and feminine singular from now on so I can ignore 95% of declension rules)
Neuter doesn't distinguish between nominative and accusative, either -- it's only masculine singular that does.
And regardless of number and gender, you'll still have to worry about the dative :)