In short, not likely to be possible using a single Airport card.
99% of the time when a workstation's WiFi card connects to a standard wireless access point, it does so in WiFi "client" mode, which has certain physical (i.e. radio-frequency) requirements.
When operating in "client" mode, your workstation's WiFi card cannot act as a repeater or quasi-router for other clients. ("Ad Hoc" wifi mode can support multiple simultaneous connections to different devices, but Ad Hoc and Client modes are mutually exclusive.)
What should work fine is for you to add a second, separate WiFi interface to your Mac, for example a USB-to-WiFi adapter. (cheap, $19! And no, I don't work for OWC.)
That independent WiFi interface can then be separately configured for Internet sharing to give your DS (or other devices) a "temporary hotspot" connection. USB 2.0 has a minimum latency of 0.125ms and an average bandwidth of 25 to 35MB/sec -- probably plenty for your gaming needs, unless you're going to be connecting more than 3 or 4 clients.
Also, this question is closely related to Wi-Fi Connection sharing on Macbook Air via USB dongle , which is still unanswered.
Your messages says it clearly.
Your Internet can not be shared!
It is prohibited to do so by a set up called 802.1x.
Your network administrator(or you) has created the 802.1x configuration profile to connect to 802.1x type network.
That profile does not allow you to share wifi (for security reasons).
If you have access to the 802.1x then you can change that.
If you do not have access:
Try creating NEW Location ! (without the 802.1x configuration).
Under Apple(top left) select Location > Network preferences
In the new Network window click on the Location then select Edit..
Now click on the (+) to add new location (name it)
Now select (add with +)the wifi to use, and add Bluetooth PAN (with (+))
Now go to sharing and Enable Internet sharing with BT PAN.
Do not forget to turn off and turn on the WiFi to enable it.
Best Answer
While Wi-Fi is the internet connection path, it cannot simultaneously share internet from the same interface.
This is similar to iOS's feature, where turning on Wi-Fi disables hotspot.