I'm puzzled about why this question has been closed.
IMEO, identify-this-game questions should be closed if they have so few details they can "match" multiple games; while I agree that the linked question is vague at best, it contains some elements that are very unlikely present in other games. This means that if someone who has actually played that game notices the question, he can answer, and the answer will be correct.
I agree that this question is probably answerable, as is, by someone who remembers that game well. On the other hand, I feel that sometimes we just have to draw the line when a question is too vague, among other reasons because the more vague it is, the less likely it is to ever be useful for anyone else.
In this particular question, the fact the OP hasn't supplied a year, or even a decade, is already alarming. And he "thinks" it was a pet Rhino. And he remembers one very short puzzle (?). He provided no information about gameplay or perspective, which I consider important. And his comment about the art style is very vague.
There's two distinct possible bad avenues that an "identify-this-game" can go. The one you're noting is when the details match way too many games, then it is difficult to narrow down the target.
The other possible avenue is when the details don't match any game. This is the hardest criteria to judge on, of course, being that it's on the same lines as proving a negative. But this was, as it were, the biggest issue with identification questions and the one thing that Jeff Atwood especially didn't like about them - these are susceptible to whatever whims and distortion that memory provides. What even sticks as a very distinct detail may even be completely false.
I'll recant a memory I had of doing an identification question on an IRC channel years ago. I wanted to recall an SNES platformer I had played in my youth, which I recalled two distinct elements. You had a selection of tools you could switch through at the top of the screen, one of which was something like an exploding lollipop. As well, the character herself was a some sort of cute valkyrie girl, and one the first stages was shining castle.
Someone did know what I was talking about. The game ended up being Magical Pop'n, which stars a little blond magician girl veritably wearing a blue version of Link's outfit, and the stage I had thought was a brilliantly colored fortress was actually... a city and its sewers. Memory does that, y'know.
Or if we want a more local example, take this question. The key identifying point to distinguish itself from other animal racing games is the firing of monkeys. Except they weren't monkeys, they were hedgehogs. There are a lot of other identifying factors one might've provided (the moose's name was Morris, matches were one of the best weapons, etc.), but the combination of a whole lot of details and date got the game a lot easier than if it had just been a scant few.
Until the actual game is revealed, it is difficult to assess what details are fact, and which are whimsy. That's why having a lot of different details such as date, platform, style, and everything else is important - no matter how specific or unique a single piece of detail is, if it's completely wrong or otherwise inaccurate, then it's just leading everyone on a wild goose chase. Sometimes, there just isn't enough information provided in a question, whether it is to distinguish itself from other games, or simply to be identified for what it is.
