Meh... yes and no. But basically "no".
Yes, technically the term "alloy" may be inappropriate, but no, we are talking of a crude combination of iron and steel, not pure steel, not even remotely close. An "inclusion" might be a more technically accurate term. So, "steel" is indeed an anachronism, as we think of it today, as the term is usually used.
What the Crusaders called "Damascus steel" is (probably) not "steel" at this time, not the way a blade or tool is steel today - they just (almost certainly) didn't have the technology to melt iron, which is what's required. No cast iron = no pure steel, it's just that simple, and there's no hard evidence of either, not in final form, not in records, not in archaeological evidence - nada.
Here's how it works, the nuts and bolts:
(And the below is all "with no magic" - we're talking about the RL history of steel. Ysmv.)
A carbon/Iron mixture can produce a number of types of end product alloys - wrought iron, steel, cast iron, pig iron, etc, and these are distinguished by their % carbon content. Such an alloy is considered to be "steel" at around 0.5 % - 1.5% carbon. And that was impossible to achieve in the 1200's with any true "homogeneity", and would be for centuries.
A medieval "weapon smith" starts with iron, from ore, so about as pure as you can get it. That's "wrought iron" ("wrought" as in "worked by hand"), and soft, and less than .2% carbon, and that only by accident of smelting.
Since there are no blast furnaces, the melting temperature of iron can't be reached*, so the only way to get carbon into the mix is at the surface. The smith can "carbonize" the surface, but only the surface, and do some folding, and repeat. A lot. This is the classic Japanese technique. Master medieval "steel smiths" had secrets for carbonizing the surface of an iron weapon more effectively as it was being worked.
[i](* This is not a 100% guaranteed historically accepted fact. It's possible there were secret techniques in remote and distant corners of the map, or "lost techniques of the ancients", etc etc. But it's the general consensus, and no hard proof otherwise exists.
By the late 1300's, Europe had furnaces that could just barely melt the surface of iron, and improve this process. This is what is believed to have been known earlier in "Damascus" - but it's unclear exactly what they were doing. Again, better, but not true, pure "steel", not even close at this point. After blast furnaces, late 1700's-early 1800's, you could get up to 4%+, cast iron - "cast" as in "poured molten into a mold", and steel was then merely a matter of controlling the process and keeping the % around 1.0.)[/i]
But regardless, the end product is not "pure steel" - it's iron folded with microscopically thin layers and random bits of steel crystals mixed within it. The master weaponsmith's secret art was making these atom-level surface-layers as even and dense as possible, and the patience to fold it again, and again, and consistently. Fold something 10 times, you have 1000+ layers; 20 times is 1,000,000+. Very close to "homogenous", even if not truly such. The classic watery pattern on damascus and Japanese katanas shows this folding and layering.
So - is there steel in the metal? Yep! Get a microscope, we'll show you the steel crystals. Is the blade "steel"? Nope! It's iron - but even with the microscopic amounts of steel chunked semi-randomly in next to that iron, it's hella better than anything else.
So "steel", "steel weapons" and "steel armour" are an anachronism, even in Damascus (most probably). Extremely high quality improved iron weapons are not.
(And then you mix that with magic, and you're home.)