As of now these features will continue to work. By announcing these deprecated features, Microsoft is providing enough notice for all of us to either remove or replace them.
Dialogs are now being deprecated and can be replaced by using Business Process Flows or the new Mobile Task Flows. Dialogs were introduced by Microsoft starting Dynamics CRM version 2011.
Service level agreements (SLAs) are a formalized method to help organizations meet service levels when they provide customer service and support. They are being replaced by Enhanced SLAs.
Mail merge had many limitations and was cumbersome to use. Instead the new Word Templates functionality can be used.
Outlook Client should be replaced by the new Dynamics 365 App for Outlook.
Relationship roles should be replaced by Connection Roles.
HTML 5 should be used instead of Silverlight in web resources.
Email router should be replaced with server-side synchronization feature. This feature is easy to use and configure.
Service Scheduling using the Service Activity should be replaced by Unified Resource Scheduling included with Dynamics 365 for Field Service.
Parature can be replaced by Knowledge Management feature.
Announcements never really provided any value within CRM and will be deprecated.
Some of the Client APIs are deprecated in the current release to reorganize the Xrm client API object model to better align with the need of using the same client scripts without having to change them based on the context or the client (web client or the new Unified Interface) where they run.
This has been replaced by Entitlements in Dynamics 365 for Customer service.