Try with sort(1):
sort -rt';' filename | sort -t';' -usk1,1 Aerial Assault (USA);Aerial Assault (USA);Sega Master System;;1990;Sega;Shooter;;;;;0;;;;; After Burner (World);After Burner (World);Sega Master System;;1988;Sega;Flying;;;;;0;;;;; Air Rescue (Europe);Air Rescue (Europe);Sega Master System;;1992;Sega;Shooter;;;;;0;;;;; Aladdin (Europe);Aladdin (Europe);Sega Master System;;1994;Sega;Platform;;;;;0;;;;; Both sorts will use the ; as the field delimiter (-t';'). The first will reverse sort (-r), so that the empty fields come after the non-empty fields, and the second sort will sort by the first field (-k1,1), and remove extra lines with the same first field (-u = uniq), but will otherwise keep to order set by the first sort (-s = stable).
This assumes that instead of the "longest" line as the title says, you actually want the "most complete", ie. between two lines with the same first field, the shorter one has always a subset of the fields of the longer one (which is the only case where discarding the shorter lines can make any sense IMHO). It also assumes that your sort implementation has a -s (stable) option: both the GNU (Linux) and BSD sort do.
If you want to do it on a batch of files, you should use find:
find dir -type f -name '*.txt' \ -exec sh -c 'for f; do sort -rt";" "$f" | sort -t";" -usk1,1 > "$f.new" && echo mv "$f.new" "$f"; done' sh {} + Adjust the find's predicates (-name, etc) and only remove the echo from before mv if you're ready to clobber your existing files.