I just came from a game where we had Ad Janna top, no jungler (i was the mythical river shen), and didn't take a single dragon until the 55 minute mark. At the end of the game our ezreal had more kills than Jinx, but that was because he just has the stronger late game. Jinx became much more fed much faster in the game. The enemy team gotten the 5th dragon stack buff twice and we still managed to win despite losing almost every teamfight except for one where we caught them at baron. How did we do this? Coordination and Communication aka teamwork. What we did was we sent 4 people to distract the enemyy team while sending another person to splitpush. We would roam as a group catching people our whenever the enemies split up. We didn' win though a superior team comp or by getting our adc fed. We won by working as a team.
Also looking at your game, a vast majority of your teams kill are on you and only you. Over half the teams kills were ones you had, meaning an incredibly large chunk of the teams power was focused in you. The enemy team balanced out their kills more. Akali had 14, Jinx had 14, and Udyr had 10. That means the enemy had 3 potential people who could be a serious threat in a fight. Now without seeing the actual fights themselves I can't make any definitive claims about where you could have given the kill to someone else, but keep that in mind.
In the end if you really despise adcs so much go play teemo. I had a teemo support go 2/20 in lane to the enemy adc, but manage to 1v1 her late game and win because of the blind. That is not even an exaggeration on the amount of kills. He ended the game about 7/27/14 and the final score was 55 kills our team 90 kills their team, but somehow we won. Weird shit happens sometimes.