Service Fabric is not equivalent to Lambda, we have Azure Functions for that. SF is a cluster orchastration framework (think mesos) and it also has a rich .net and java sdk for developing Microservices that will be orchastrated on the cluster. it can also run exe \ containers. it is not server-less at all. It is nothing like API Gateway.
App Services is just web site as a service. I wouldn't call it PaaS but I understand this term is subjective.
Cloud Service is an old concept that we never recommend for new workloads, so I think it doesn't belong on this article.
Virtual Machines is self explenatory and it's very much like EC2 unlike who the article present it.
API Apps is not a proxy, it is an API. You could host you web API (any web framework) here. It is the same as website but with some semantic difference and cool swagger integration.
Virtual Network is not just for hybrid scenarios, it is the fundemantal container of all IaaS based resources in Azure.
Traffic Manages is not a like a classic Load Balancer (as the comparison suggests). It is a "Smart DNS" service for multi-region geo deployment.
Data Lake Analytics foes not "hold" any data. Data Lake Store does. Analytics is a batch processing technology that can process data from Store, but you can use Spark or whatever to do that as well.
Data Lake Store - see above. I think they confused this one with Data Factory.