They probably call them serverless because you are mainly billed by the number of requests instead of the number of hours it runs for (although for Dynamo, there is a cost per table and r/w)

Would we lose any meaning by just calling DynamoDB and S3 managed solutions, like in the old times?

EC2 is a managed solution but you still need to manage servers.

Elasticsearch and RDS are also managed, but not serverless.