Summoner DPS is all about maintaining the highest possible output and never letting anything run out. This means keeping your 3 main DoTs applied Shadowflare up, and spaming ruin.

Essentially time you have to spend reapplying DoTs and shadowflare is time that you're not using ruin. So spellspeed is helpful in that it lets you get your DoTs back up quicker, so that you can go back to spamming ruin. Spellspeed will also increase your ruin output which will increase your DPS even further.

Also if I'm not mistaken, spellspeed increases garuda's regular attack speed as well.