What kind of backend is the dataset? is it excel or csv ? if yes, then may be its already spiced and thats the reason why its not working since you would need to have the data refreshed to have the alert triggered.
Note : File based data set cannot be refreshed since file/data never change once its uploaded.
When you create an alert, QuickSight checks your data for any breaches against the thresholds you set based on when your dataset is scheduled to refresh. The information presented in the alert varies based on the visual type that you’re creating an alert for. For SPICE datasets, alert rules are checked after a successful refresh of your SPICE dataset. For direct query datasets, alert rules are checked at a random time between 6:00 PM and 8:00 AM in the AWS Region that holds the dataset by default.
Are you the QuickSight Admin within your Org ? if not may be check with the QS admin in your organisation.
Alert Permissions
If you’re an administrator, you can control who in your organization can set threshold alerts in QuickSight by creating a custom permissions policy. To set custom permissions in QuickSight, choose your user name at the upper-right corner of any QuickSight page, choose Manage QuickSight, and then choose Manage permissions.
Please help me understanding the issue here. The pic -1, I can set the alert where in Pic 2 the pivot does not have any option to set the alert!!!
Pic-1