Does this influence the usage of the PLUGIN on my WordPress website?
Yes, it does. I received the email from Google too, today, and I am yet to assess its impact.
However, a cursory glance at it indicated that the Picker API was lacking in several features, such as the ability to pull photos from albums. I know that the email that they sent says it is possible, but the documentation for the API has no such information.
This is the third time that Google is making a huge change in its API – the first was when it changed how to pull photos from PicasaWeb, the second was when it junked the PicasaWeb API altogether replacing it with the current Google Photos Library API, and this is the third.
To be honest, I am unsure if I will be able to make the switch without degrading user experience – as it is, Google has the worst onboarding experience of any platform, and I don’t see their Picker API making things easier.
In the worst case scenario, I will have to stop developing for Google, but it is too early to say conclusively.