Confused with understanding a recommended signal conditioning interface
You would be wise to include at least another passive LPF in the receive port to avoid an ECN on cuts and jumpers.  Because you will get some noise with a high speed ADC from the cable acting as an antenna.

1) First of all 360 deg pots have a limited rotational life and even less with constant dither back and forth.  This life is reduced further if there is any significant current flow in the wiper at the terminals. The shunt cap can cause thus current when dithering between +V and 0V hence why the 1k series R is suggested limiting current swings to about 12 milliamps into your load cap if it oscillated back and forth near North where terminations are located.

side info

Given this sensor has a 8 degree deadband this matches up with Wirewound Bournes pots worth about $25 in volume. They are rated for 500k rotations with no load current but nothing said about oscillations.  Whereas Conductive Plastic circular pots tend to have a deadband of 20 deg but rated for > 2 million rotations.

2) 270k ohm is recommended , perhaps , for using bipolar input bias current induced offsets which can be minimized by selection of suitable types or by matching your feedback R and then considering input offset bias currents or by choosing FET input Op Amps. Otherwise, bigger R could mean more input voltage offset.

3) I'm not sure of the chance of miswiring the wiper to Vcc or 0V in the field, but a 100 Ohm  current limit resistor prevents wiper damage if that happened. Since 200 ohms adds to the 10k ohm by 2% this introduces attenuatuon error but then reducing the range from 360 deg to 352 deg increases the sensitivity by 360/352=1+2.27% so this cancels this attenuation error pretty well.

4) Buffering depends on Op Amp's ability to drive a long cable capacitance. For EMI reasons long cable with high input impedance are prone to significant EMI interference. So depending on proximity of noise to the cable, a buffer with low impedance over the noise spectrum, or a CM choke with shielded pairs or other considerations.

p.s.

One better way to implement wind direction as our team did in designing Met. Canada remote weather stations used a "Grey Code" rotary encoder. (circa '75)

These days the optical quadrature encoders with 1000 pulse per rev is owned now by Broadcom (once HP) that use these encoders and a special CD with the patterns for about the same price as a Bournes WW pot.

p.p.s.

Many students and young engineers fail to recognize how important it is to eliminate Common Mode (CM) noise at the source, especially SMPS ground currents and the routing of ground.

Consider if you have a SMPS with considerable common mode noise . This conducts along the coax shield and couples to the high inpedance input via the cable capacitance of ~100 pF/m thus 50 m sees CM Noise coupled to your input signal at some f via 5000 pf which is some Zc(f) switching frequency, lets say 50kHz. So the cable acts as a shield for outside radiated noise but now becomes a path for conducted ground noise. Now the source impedance of your driver if it were 50 Ohms would permit an EMI ingress. You may need a low pass filter at the ADC or a CM choke since you have a high impedance input and a non-zero impedance source and a possibility reflections. Also any linear driver or buffer has an output impedance will rise from near zero to high values (xx ohms) at it's unity gain bandwidth.

Often people prefer shielded balanced pair to avoid these coupling problems and do not earth ground signal ground at source.