Line-of-sight (LoS) multi-input multi-output (MIMO) systems exhibit attractive scaling properties with increase in carrier frequency: for a fixed form factor and range, the spatial degrees of freedom increase quadratically for 2D arrays, in addition to the typically linear increase in available bandwidth. In this paper, we investigate whether modern all-digital baseband signal processing architectures can be devised for such regimes, given the difficulty of analog-to-digital conversion for large bandwidths. We propose low-precision quantizer designs and accompanying spatial demultiplexing algorithms, considering 2x2 LoS MIMO with QPSK for analytical insight, and 4x4 MIMO with QPSK and 16QAM for performance evaluation. Unlike prior work, channel state information is utilized only at the receiver (i.e., transmit precoding is not employed). We investigate quantizers with regular structure whose high-SNR mutual information approaches that of an unquantized system. We prove that amplitude-phase quantization is necessary to attain this benchmark; phase-only quantization falls short. We show that quantizers based on maximizing per-antenna output entropy perform better than standard Minimum Mean Squared Quantization Error (MMSQE) quantization. For spatial demultiplexing with severely quantized observations, we introduce the novel concept of virtual quantization which, combined with linear detection, provides reliable demodulation at significantly reduced complexity compared to maximum likelihood detection.