This is a known bug on the Swype website. They have posted a workaround which I tried and it worked after several attempts:
"Unable to install Swype on MIUI Rom
When Swype is installed it needs to be unloaded from Android at the time the Swype Installer passes the authentication key to the Swype program. MIUI attempts automatically load and enable any input device into memory as soon as they are available. Because of this there is no reliable way of getting Swype working on MIUI, and even if you do it may not stay enabled for long.
However if you'd like to try, Android Peak has developed a workaround that works some of the time.
UPDATE: marchief has found a workaround which does not require the use of Titanium Backup, may produce more consistant results:
Download installer
Download and install swype
At the enable step leave the installer and select swype as the input device
Reboot your phone
After Reboot, open the swype installer again
Select "Select Android keyboard" and change input back to android keyboard
Choose disable swype, go to applications and uninstall swype but NOT THE INSTALLER
Go back to the installer and generate license
This should put you through the download process again so just follow it and re-install swype
Once re-installed it should generate the license, but it still won't work
Reboot your phone again and all should work, enjoy!"