Differentiaion is definitely one reason OEMs design their own ASICs, but there are many more: 1.) Design control 2.) Long term supply stability 3.) Price. 4.) Power 5.) Cost 6.) Performance 7.) Density 8.) IP Protection 9.) Time to market
There has been a lot of hype in the last N years proclaiming the "death of the asic", and yet there are still plenty of monster ASICs being built by tier-one vendors.(especially in the comms field) Sure, ASICs are now more expensive to build ($5-10M) but they still make sense if they can be used to gain or keep revenue shares in end equipment markets that are in the $B's.
Maybe ZTE wants to better protect their design from a copycat. If they used a standard SRAM-based FPGA and a standard DSP it would be easy for someone to copy or reverse engineer their design. With their own ASIC they can better protect their design from possible theft.