He didn't really though, he was winning the fight quite comfortably and had 2 knockdowns against Parker who'd never been knocked down before amateur or pro prior. He gassed at the end, got caught and took a knee and tried to hold to buy time. He still won clearly.
Whyte certainly has flaws, his stamina can be called into question and he can get caught with shots too. He got knocked down by Rivas too but didn't look extremely hurt then and won the fight easily. These vulnerabilities can make the fights compelling, nobody in the division is without flaws, Fury also got knocked down prior to Wilder by Cunningham and Pajkic, he may appear to be the man right now but he's not invincible. There was a chance that fight vs Wallin could have been stopped if Wallin was better and a bigger puncher.
That's what makes this shyt interesting, none of these fighters in the heavyweight division currently are invincible, all have flaws. Fury would start favourite vs Whyte but Whyte definitely poses a threat and would definitely be within the top 3 fighters Fury has ever fought thus far.