The club aren’t writing a cheque for £250k as such. Rather they have agreed that the central football piggy bank (the premier league) can make this extra payment from funds which the clubs might otherwise have dibs on.
From the small(ish) print:
“Scudamore, 59, will receive the money from central Premier League funds rather than the proposed £250,000 from each club — even though each club will effectively lose that amount each.”
So in essence, what’s happening seems to be that the overheads of the EPL will increase by £1.66M each season, meaning there is less left in the pot to distribute to whichever clubs happen to be in the EPL that season.
Since it was a vote by the EPL members its probably impossible that any one club could refuse to pay it because technically, they aren’t actually making a payment.