"由店家出钱" can be translated into English as "The expense is covered by the shop/store" or more naturally in some contexts as "The shop/store will foot the bill."
Here are two example sentences to illustrate the usage:
1、 In this promotion, the expense is covered by the shop.
(在这次促销活动中,由店家出钱。)
2、 Don't worry about the cost; the shop will foot the bill.
(别担心费用,由店家出钱。)