Magma is hot, but unless things have changed recently, it only heats surrounding tiles to 'kinda warm'(so you could, say, fill a magma channel under your water moat, and the water above the magma shouldn't freeze in the winter, but wouldn't boil off either) - to keep things near magma from melting, bursting into flames, etc.
Which would be cool, but bothersome; magma forges would be useless, and even walking over the magma channel on the z-level below, floor intact, would cause a dwarf to combust, while pumping would have to be powered(and need a magma-proof axle), tho channeling magma itself could still be done decently well, albeit always needing a sacrificial dwarf.
Thus to melt most things, or set them alight, the magma has to get into the same tile space. Which is why anything that blocks fluid-flow will stop magma, no matter the material, as the magma never enters the same tile - thus, your wooden floodgate is only 'warmed'.
Deconstruction of doors and floodgates(etc.) made of magma-proof material generally happens when they're connected to something that isn't 'proof, and which is then destroyed/melts when magma enters the tile - typically, this is the mechanism controlling it, for as that [B ] tag shows you, it's 'part of' the door/floodgate/etc.
Thus your steel floodgate /w slate mechanism, as well as your wooden door, will hold back the earth's fiery blood forever, until they're opened, at which time the wood will burn and the slate will start to melt(actual melting takes time, remember; note those stones in your filling magma channels - this causes confusion as people open floodgates built with non-proof mechanisms, and don't notice anything wrong until they check up on it a while later, as the mechanism survives the magma for a little while, so everything looks fine at the time), and you'll be left wondering how to recover that deconstructed steel floodgate.