You say on your last device there was an option to change default storage to SD. What I've found is some apps will allow you to move their core to SD, which is an option I've used from the App Manager (Settings>Apps>All). In app you will sometimes be given the option to save to a location, depending on the app. I've even seen occasion when you can move a folder to a new location and the app is able to recall the data however this is rare in my experience.
The only two things I can think of to try in your example is 1) move the apps core with the app manager, this could cause it to start saving to a location on the SD as a result. 2) Save the folder to the root of the SD, so it would look like SDCARD/Folder X. Because looking at your example I'm assuming that Obb is the game in question and you've saved the Obb in a folder.
One other thing, and I'm sorry I can't check it right now, but check your Google Play settings and see if you can default new installs that allow move to SD to default to SD. I thought at one time when move to SD was picking up speed that was an option but I could be wrong.