Does your arsenal include livestreamer and/or streamlink? Both of those should work.
Code:
livestreamer "akamaihd://https://livestream-f.akamaihd.net/3161248_7527687_lsi0yk3w5u7vpbzvs00_1_2320@408235 swf=https://cdn.livestream.com/media/player.swf" best -o game.flv
Use the above akamaihd url if the livestream page url doesn't work.