Search the web on the term "stove guard" there are quite a number of products made for this exact purpose.

And the photo of the offensive area is................?

You would not want to place anything flammable against the back of the range. Nothing closer than at least 6", unless it's fireproof. So, unless that buffet is made out of stainless steel, keep it away from there. The best thing might be a portable standing screen made from metal that could be folded against the back of the range when it was in operation, and be decorative when not needed. Maybe make one out of copper plumbing pipe, copper roof flashing, and wire to whipstitch fasten the sheeting to the pipe frame.

Is it possible to build a narrow table (10 to 12 inches) that would back up to the stove? Top it with a piece of stone or ceramic tiles.
Or you could attach a small narrow counter top to the back of the cabinets. Talk to the landlord if you decide to attach it to the back of the cabinets on either side of the stove. Maybe he will split the cost. It would be an improvement if you have the room.

You're moving into an apartment that has a kitchen that is not to code anywhere, even Georgia. You don't have to do anything put pick up the phone and call your landlord.

Maybe the landlord would put back the wall that he took out?

You all are so helpful! Thank you.

In reply,

it is a house, not an apartment.

It does look like someone took out the wall? Maybe began a remodel they didn't finish?

The buffet is shorter than the counter top on which the stove top is positioned - it could serve as a barrier, at least temporarily, to keep young hands away.

I am curious about whether this is indeed not to code and will research this.

I'd probably stick a metal baker's rack behind it. Will you still have space in the dining area if you put something there?

Even large a potted plant on the floor could keep people from getting too close. I suspect it won't be as bad as it seems once you get in there, but something on the floor to keep people from standing there is probably all you need.

I'm guessing there was a breakfast bar on the other side of that at one time.

Could u put a piece of tempered glass behind it?

Did anybody actually Google "stove guard?"

There's one kid that ought not be running around unsupervised.

No, am I remiss for not doing so?

I once watched a photo shoot for a child safety outlet cover. The photographer had to train the kid to try to put his fingers in the sockets. When the shoot was over, his mom couldn't get him to stop. Good times.