Can I get the data from the Matomo API web services and publish, reuse, process this data in a non GPL software?
Yes, the data coming from the Matomo (Piwik) API belongs to you and is not covered by the GPL.
You can use Matomo as a service, and reuse, publish, display, modify, process the data coming from the Matomo API using the REST API web services call. See also the GPL FAQ: Is there some way that I can GPL the output people get from use of my program? For example, if my program is used to develop hardware designs, can I require that these designs must be free?