Why do retailer want you to open a credit card with them and not their competitor?

There are several factors.

If the card can only be used at their store, then they're effectively making it easier for you to shop at their store than at their competitor's store. I hope the reason they would like this is obvious.

Also, they get to charge interest. Interest on a credit card is generally higher than interest on a savings account, so for them it makes some amount of sense to have their money invested there (plus which, the item cost them less than you bought it for, so they're effectively getting a double bonus).

Finally, by using their own card instead of a generic card like Visa or MasterCard, they get to avoid the "merchant fees" that those companies charge retailers to accept their cards (you may not have been aware of it, but if you pay with a credit card, the vendor has to pay the credit card company a portion of the transaction. This is why some places offer discounts for cash; if they have to pay 3% of the transaction to a card company, it makes more sense for them to give you a 2% discount for paying cash, because then they get 98% of the full price instead of 97%.)