If you are not using the serial daisy chain then you can leave the SDO pin open and not have to install a pullup resistor on this pin.
The AD5290 part is designed to allow its use in analog circuits that have power supplies up to and including +/- 15V. This allows the "digital pot" terminals to connect into OpAmp circuits (and other similar types) that operate on voltage rails of this magnitude.
The main reason that the SDO pin on this part is open drain is that it allows the device to be built into a package of 10 pins and eliminates a need for a digital logic level supply pin. If the SDO pin (the only digital output on the part) was designed with a push-pull output then the extra digital supply pin would be required.
As others have stated the open drain nature of the pin is such that the pin could be be tied together with multiple other open drain outputs but that has very little utility in the use of this particular part. Instead it can have a role in the daisy chain operation when the digital supply levels are other than a 5V supply. A close look at the VIH and VIL specifications for the part will show that the inputs to this device can be driven equally well from a digital realm of 5V or from 3.3V.The open drain SDO can be externally wired up to a 5V or a 3.3V pullup with equal utility depending on which digital rail is used in the system.