Every hero can beat every other hero. It's all determined by a number of factors. Use of positioning, mechanical aim, ability management etc. It's all determined by the skill of the players.
It's an uphill battle, but yeah he can. Winston's 80 burst damage (jump, quick melee, land) combined with his native damage can make its way through 250 HP pretty quickly, especially if it's an unconfident Doomfist.
your head is the size of a very large melon and you have no real way to avoid rocket punch beside jumping. You'll be juggeled to dead if both of you 1v1 at same health.
The problem is that doomfist generates shields so fast that Winston will have a tough time. But if he lands his jump packs he can potentially out burst it.
usually doomfist takes it easy and if u disagree uve never seen a good doomfist play ... like he bassically gets fucked u less he uses his bubble perfectly