If I saw "spoon", I'd assume that they meant "the actual spoon I use to eat cereal in my drawer" rather than either tsp or tbsp. The point is that the recipe author doesn't know what the right amount of that spice is. They can't know because the spice sitting in your cabinet is almost certainly much less fresh than what they have in the kitchen.
Spices tend to be flexible outside a few exceptions. I'd wager that you can just wildly change almost any spice amount in almost any recipe before you've ever made it and and have any sort of calibrated taste it'll turn out fine. Salt is a way bigger risk here and not many recipes give precise salt measurements.
In this case the ambiguity is a factor of 3X, the difference between a teaspoon and a tablespoon. Or possibly more: given the quantities of the recipe he may mean some kind of personal dedicated spice spoon that could be around 1/2 tsp. In which case a tablespoon would be a factor of 6x, which is sufficient to make a recipe inedible.
If that recipe appealed, I would say that if you use a teaspoon the recipe would work (assuming he hasn't made other errors in the recipe; I didn't look that closely). But he's not following the conventions and I'd probably go looking for a difference recipe.
Once you've made a few recipes successfully you can, as you point out, easily halve or double spices. But I'd start with recipes that were better tested than this one.