If a big box rents, do they typicaly get the right to exclude competing tennants in the same center?

No prospective tenant “gets the right” to exclude competitors, but they certainly will ask for that right in the lease. Then it is up to the landlord to decide whether to agree. If the landlord wants the big box tenant, he’ll likely agree to the demand. A tenant selling home appliances won’t want to be in a center that has multiple appliance retailers because that cuts into his sales. So you can bet the tenant will ask for the exclusion, but it’s the landlord that decides if the exclusion is granted.