how to run awk twice across the same file

I would use two arrays:

awk -F, '{a[$0]=$2;if($3=="win")b[$2]++}END{for(i in a){if(b[a[i]])print i}}'

Is there a more elegant way to do this?

Yes, of course there is. Just run Awk twice across the same file (as you said in your title).

awk -F, '$3=="win"{won[$2]} FNR==NR{next} $2 in won' log.csv log.csv