The Games pitted Team GB against teams from the Cayman Islands, Austria, Bharat (India), Slovakia and the Czech Republic.
Parker scored two goals in Team GB’s seven matches as the Team GB seven-a-side Unified Football squad made the final of the competition against Austria.
After beating their European opponents 1-0 in the group stages, hopes were high that Team GB would win the gold medal.
However, despite a half-time pep talk from Olympic boxing champion Audley Harrison, Team GB went down to a 2-0 in the final.
Parker, 19, said: “It was a fantastic experience and the whole team are on a high after winning silver.
“Even though we had already beaten Austria earlier in the week, they seemed more up for it in the final, and at half time we were 1-0 down.
“During the interval we had a pep talk from former European heavyweight boxing champion Audley Harrison, who put the fight back in us, and we went out in the second half with a totally different frame of mind and really pushed for an equaliser.
“However, Austria kept the pressure on and sealed the game with a superb second goal minutes before the final whistle.”
More than 7,000 athletes from 170 countries competed at the World Games across 28 different sports.
Parker, who is undertaking a business administration apprenticeship with Disability Action Yorkshire, in Harrogate, added: “Whilst it was the third Special Olympics I’ve competed in, it was the first World Games.
“The host town was brilliant to us and we were made to feel incredibly welcome indeed. I’ve made new friends with many fellow Team GB athletes.”
Jackie Snape, Disability Action Yorkshire chief executive, said: “Everyone here is extremely proud of James’s achievements.
“We followed each match and were thrilled when he scored twice against The Cayman Islands. Even though Austria won in the final match it’s still a great accomplishment to finish in silver.
“James is proof that a disability should not stand in the way of your dreams. His success is one to be admired and celebrated.”