You are confusing two types of driver. The driver for the firmware (rtl8192cu) of the wifi device has nothing to do with the driver backend of wpa_supplicant (nl80211). Let's explain in detail.
Behind the link you have given it is said:
Make sure to blacklist the older rtl8192cu driver, which some distros seem to load by default otherwise.
Seems Raspbian is one of these distros so you should follow it. Before doing it we have to check that the new rtl8xxxu driver is available. You can do it with:
rpi ~$ sudo modprobe configs
rpi ~$ zcat /proc/config.gz | less
In the pager search for
CONFIG_RTL8 and you will find
CONFIG_RTL8XXXU=m that means the wanted driver is compiled with the default kernel and available as module. Just try to boot with blacklisted
rtl8192cu and look what driver is loaded. Maybe you have explicitly to load
rtl8xxxu. I suppose you know how to do it with files in
/etc/modprobe.d. But just looking there from a default raspbian image I see:
rpi ~$ ls /etc/modprobe.d/
blacklist-rtl8192cu.conf blacklist-rtl8xxxu.conf ipv6.conf
Seems both drivers are already disabled. I don't know why do you see that
rtl8192cu is loaded on your RasPi. Just restore
blacklist-rtl8192cu.conf and rename
blacklist-rtl8xxxu.conf maybe to
blacklist-rtl8xxxu.conf~. This should load the new driver
rtl8xxxu on boot.
Now to come to the driver backends for wpa_supplicant. Within
man wpa_supplicant you will find:
[..] Support for each of the driver backends is chosen at wpa_supplicant compile time. For a list of supported driver backends that may be used with the -D option on your system, refer to the help output of wpa_supplicant (wpa_supplicant -h).
wext is the predecessor of
nl80211 and mostly only used for backward compatibility. Default is
nl80211 and you should use it at the first place with the option
-D, for example with:
rpi ~$ sudo /sbin/wpa_supplicant -c/etc/wpa_supplicant/wpa_supplicant-wlan0.conf -Dnl80211,wext -iwlan0 -B
This is the default setting for running wpa_supplicant on Raspbian so you haven't to worry about it.