2x2 Mimo antenna layout: Is it a requirement to length match the antenna traces
It's not necessary to length-match the antenna's traces.

The whole point in MIMO is that an algorithm uses the fact that the two antennas are receiving different signals to do up to two things:


Diversity gain (channel influences and noise –hopefully– being uncorrelated between the two receive chains)
subchannel construction by finding Eigenvectors in the \$n_\text{TX}\times n_\text{RX}\$ channel matrix


For either thing, the actual phase of the received signal doesn't matter - the only thing that matters is that the two antennas are positioned in a matter that allows them to receive different signals (ie. don't act as part of an antenna array).


  Is there any advantage to a length matched antenna pair?


If you interpret that algebraic subchannel-extraction spatially, you end up doing digital beamforming. Same thing, different kind of perspective. 

If you then can relate the phase seen at one antenna to the phase of the same signal seen by the other antenna(s), you can actually deduct an incident angle, or, inversely, send a beam into a specific direction. 

Again, this doesn't demand equal, but known length traces. But matched will do as "known" :D


  This design is required to specifically measure RSSI.


RSSI doesn't actually mean anything unless you specify which signal and which measurement methodology you use! 

So, assuming you just simply want to maximize SNR, make sure you place the antennas more than half a wavelength apart, and if possible, use different polarizations, directivities etc to increase the independence of the observations.