It's a different plant. Hell it looks more like joint grass than wheat. And if you look at the wiki entry, it was hybridized from other grasses. It is no different than the wheat we have now. You just happen to not be allergic to it.
And how do you know you're allergic to all modern wheat? Is it hard red winter? Hard white winter? Spring hard wheat? Spring soft wheat? All of these things are actual wheats. And you're sure you're allergic to all of them?
Look. You found a plant that you're allergic to the seeds from. You found a different plant that you're not allergic to the seeds from. That's all that's going on here.