I can't use the bing map SDK
Bing Map SDK is used for previous versions, in UWP app we have MapControl instead. And the animations you mentioned are not provided by SDK, they are just animations in UWP app. So actually you don't need use the Bing Map SDK as what you want has no relationships with the SDK.
Anyone can help me with creating path animations a pushpin on the XAML map control
This article you provided already taught about creating animations with Maps. But the target version in that article is windows 8.1 with Bing SDK not UWP app, so some APIs cannot be used in UWP app. Such as LocationCollection() is replaced by Geopath class, MapShapeLayer() maybe replaced by MapItemsControl class. More details please reference Maps and location overview and the official sample.
I convert some of the animations that now they can be used in a UWP app. You can download the demo here for testing.