MC has the ability to update play stats from a device that it syncs to. It is a setting for the Handheld device. But the larger issue is whether the device will read and update the [Number Plays] tag in the file so that MC has something to update to. Whether the A&K SR25, or any other A&K device, does that is something you will have to investigate for yourself. It isn't a JRiver issue. As you know, the play stats are updated for an iPod Classic, so the MC functionality works if the device supports it.
The same update play stats setting doesn't exist for hard drive locations that MC syncs to, and the [Number Plays] doesn't seem to be updated from the hard drive location back to the original files in MC. So if your device is treated as a hard drive location, Handheld Sync may not sync the play stats back to MC. I know that some A&K users have reported syncing only works when the A&K is seen as a hard drive location, just like a USB drive is, for example. Some A&K users report difficulty with using the Handheld Sync functionality. It seems that different models and firmware versions play a part in whether it works or not. However, my Sony Android phone does get recognised by MC as an Android device and not a hard drive location, even though it is also presented in Windows Explorer as a hard drive location.
So search the forum for threads about A&K devices and see if you can find out if they support Play Stats in a way MC can use. You may want to ask A&K, or check on their forums as well. But ideally, find someone who has an A&K SR25 and ask them.
As I said above, the Sony Music App on my phone doesn't update the [Number Plays] tag in the file so MC doesn't have an updated play stat to collect. However, when I externally forced the [Number Plays] tag in the file to be updated, the Handheld Sync still didn't get the updated [Number Plays] value. But the Handheld Sync errored on the sync for the file I tested, so it probably has other issues going on. Hence my comment about getting it working again, on Android.
Good luck.