I wanted to use it to access Google Places API Web Service, but I can't find corresponding class.
The documentation says:
Google APIs give you programmatic access to Google Maps, Google Drive, YouTube, and many other Google products.
The PHP Client Library does not include a class for Google Places; Nevertheless, it allows you to make HTTP Requests Directly. Since Google Places API is also RESTful (example https://developers.google.com/places/web-service/search) then you can use the PHP client library to make HTTP requests directly. Please read the documentation here https://github.com/google/google-api-php-client#making-http-requests-directly. That should get you started. I hope this helps!