i just looked at the Athena's Puzzle pattern. it definitely can be chained pieced. (which is what you described as your process. Chain Piecing is just sewing multiple pairs one after the other. you don't clip the threads between each piece until after you've sewn the whole set. hence, the "chain" of pairs that comes off your machine.)
this block could also be Strip Pieced, although it would take some pre-planning and some math. Strip Piecing is when you sew pairs of strips together and then cut them apart to get your pairs of pieces. it works very well when you're working with squares and rectangles. it isn't often the easiest solution when you're trying to get triangles or diamonds. (for me, anyway. others may have figured it out. :lol: )
the down-side to Strip Piecing is the need to plan carefully ahead and to do the math. the up-side is that you will cut your paired pieces to the right size after they've sewn, so everything is more likely to line up as you go.
it's a personal choice. if you try Strip Piecing as you make more quilts, you'll figure out for yourself whether or not it's a good method for you.