I'd look more closely. The uber credit posts to your uber wallet, you don't have to use the card to pay. This is how people get $25 in credit because it combines with the plat credit. If you go into the app, to your account, wallet and then tap on the amount in there you'll get a screen like what I've attached. It'll show you your $10 amex as long as it's been added as a payment method. Then go to balance details and it'll show you what's there. It takes the amex before the gc, all I have left is 33 in gc which it took anything over $25 from the prev bal.
Now the $10 dining credit doesn't work with uber but does work with grub hub, shake shack and cheesecake factory. Maybe something else, I always use it for grub hub. This does need to be charged to the gold because it is credited to the card by amex.