At the time you had this message you did NOT have internet access (…Check network).
That’s all.
Most likely your phone and tablet use 2 different google accounts.
Litchi should work just fine on the SM-T710 (Samsung Galaxy TAB S2)
Try version 4.25.0
You can find the download link in vico’s comment here:
After installation make sure you have:
-Internet connection
-after starting litchi, log in with the correct Litchi-account.
-use the correct google account