Those tissues are used to pointedly wipe off his hands, yes. The strangled noises continue right up until Obi-Wan cuts off Anakin's legs, at which point Jim wails Noooo and gestures emphatically to the screen.

"They can't work through that! Oh my God, why is this happening?"

Slack-jawed, hands in his hair, he sits up and laughs to dispel his own tension at You were the Chosen One! This isn't watching Star Wars anymore, it's Watching Jim React To Star Wars. At one point, you bet your ass he covers his mouth during some close-up shots of Anakin crawling on fire.

"This is so sad."