Why does this fireplace work?

The floor is one row of lower half-slabs, the back of that wall is entirely flat, the underside of it is dug out, now if you look closely you'll see that the birch logs are placed diagonally form the fire block.

Fire spreads diagonally though, so why is it not doing it here? Is this really a safe setup or is it only a matter of time before something burns? (I tested this for over 30 minutes without anything burning)

Why does this work? Is it really safe or just a fluke? I've seen similar fireplace designs fail.

According to the Minecraft Wiki on Gamepedia, fire can spread to any air block in a 3 by 3 square, up to one block under the fire, or 4 blocks above it. It can only spread to air blocks and only if they are next to a flammable block.

Using this information you can easily check if your fireplace is safe by using this command (if you don't have cheats, then you can rebuild it in a world where you do):

/fill ~-1 ~-1 ~-1 ~1 ~4 ~1 minecraft:glass replace air

It will turn any block that the fire can spread to into glass. If there are any flammable blocks that touch the glass produced by this command, then your fireplace is not safe. In your fireplace it looks like this:

There are no flammable blocks next to any glass blocks, so your fireplace should be safe.

Fire can only spread to air blocks that are adjacent to flammable blocks. A block can burn out only if there was fire next to it. From the screenshot it seems you have flammable blocks in range but you do not have air block next to them in range of the fire, that is why the fireplace is safe. You can check out this question as well for more details on fire spread: Minimum safe spacing between lava and flamable materials?