What did he mean by this?
When you are drunk you are less inhibited and will write things that when sober you would doubt. Sometimes you may write an emotional gem. Edit sober so you clear away any filler and crap your drunk self thought was good.
When I was a general's aide I once wrote a report for him to give to some visiting congressmen while buzzed on weird Korean booze in violation of a no-fun-allowed order. I got rave reviews.
Generally I avoid writing while drinking though. Gives the will but takes away the ability etc.
Except he wouldn't drink when he was writing, only after. There is no evidence anywhere of Hemingway having said what is in OP's picture.
“My training was never to drink after dinner nor before I wrote nor while I was writing." A Moveable Feast.