The probe affects the thing that is being measured. If the thing being measured was an ideal voltage source with zero source resistance, and if the probe was an ideal probe with infinitely high impedance, then the probe would not affect the thing being measured. But real sources do have source resistance, and real probes to have DC input resistance, input bias currents, input leakage currents. We model these non-ideal effects by the equivalent input resistance (or input impedance, if we're talking about transmission lines).
DC Input Resistance of 200kohm differential, 50kohm common-mode means:
Attaching the differential probe is equivalent to attaching a 200kohm load resistor between SIGNAL+ and SIGNAL-, as well as attaching a 50kohm load resistor between SIGNAL+ and GND, and another 50kohm load resistor between SIGNAL- and GND. That represents the input bias + input leakage currents drawn from the source that is being measured. This affects the thing being measured.
If the signal source was an ideal voltage source in series with a source resistance of 1 ohm, then a probe with 200kohm input resistance would decrease the measurement by 1/200000.
Transmission line termination is about preventing reflections at the receiving end of a transmission line: maximum power transfer happens when a source is terminated by an equal (well actually complex-conjugate) load impedance. At the source, the transmission line looks like the load impedance, and at the receiver, the same transmission line looks like the source impedance. So it's common to have series terminations at the source of a transmission line and shunt (parallel) termination at the receiving end. All points along the transmission line should look like a 100 ohm source driving a 100 ohm load. That's a 2:1 voltage divider. Connecting a 200kohm probe across the load affects that measurement slightly, but it's a negligible effect. If your transmission line was 100kohm terminated instead of 100ohm, then the probe DC resistance would be non-negligible...
It's basically the same thing as why a DVM or voltmeter has high-impedance inputs. Higher impedance is good.
A DMM rated for 200kohm impedance (terrible for a DMM but bear with me) would be adequate for measuring resistances up to 10's of kohm, but would run into performance limitations if you tried to use it to measure insulation resistance (>1000's of kohms). So treat the DC input resistance spec as a performance limit spec, not as a required matching spec.
The CMRR (typical) is rated for testing at 10MHz and also up to 6GHz. A probe that would be just fine at 10MHz (typical for a hobbyist white solderless breadboard) would look like a very different apparatus at 6GHz (expert RF microwave radio designer). Small variations in the dimensions and materials give rise to subtle performance differences at high frequencies.
What matters for your application (probing a 100ohm terminated LVDS differential pair) is actually the signal bandwidth. If you're running that LVDS pair at a bandwidth of 1GHz you're going to need a better-performance $$$ probe than if you were running at only 50-100MHz. A lower-performance probe would have limited bandwidth and could obscure timing details that you might care about. Same with the oscilloscope attached to the probe, wouldn't make much sense to connect a premium 6GHz probe to a 10MHz "student" oscilloscope.