How to correlate Devops deploy on demand with Agile Sprint Process
There is no "Deploy-once-a-day" rule in devops philosophy. It's more of: Deploy as soon as possible and as often as possible. Also it calls for decoupling architecture so different parts of it may be released separately and also for decoupling deploys from release.

The Deveops Handbook by Gene Kim et al.calls for modifying Definition of Done to include running in production-like environments. That is follow the devops principles all the time during the sprint.

What you want to avoid is ending a sprint with all the developers handing over their code that is tested, is working but is not integrated and is handed to other team to be deployed, somehow.

I'd argue that definition of done is : it's not done until it's ready to run in production. Once it's ready you may or may not release it depending on your specific business needs and the sprint goal but if it's not ready to be released right now it's not done.