App Data Not Restored After Copy From Nearby Device

Two possible reasons

• From Nexus help

When you set up your phone, you can quickly import Google Accounts, backed-up apps, and data from your current Android device to your new Nexus phone by using Tap & Go.

(Emphasis Supplied)

Kit Kat didn't have the cloud backup, IIRC, so it can't be whereas whatever is backed up is Google account stuff

• Again from Google help, of you scroll down the long list of complaints, you will notice problems when both the devices were not of same version. This cannot be concluded as the main cause as it is not documented officially, but the first one is more likely IMO.

On a side note, transfer from Huawei device on KitKat to Lollipop worked but not KitKat to Marshmallow (personal experience), that's why I was sceptical about it in answering your earlier question