Acho que isso é um problema do Ubuntu, porque no mesmo laptop não tenho esse problema no Windows.
Ao tentar compartilhar uma janela de aplicativo no Chrome, nenhuma janela está disponível.
Saída dos drivers de vídeo:
SCSI
*-display
description: 3D controller
product: GM107M [GeForce GTX 960M]
vendor: NVIDIA Corporation
physical id: 0
bus info: pci@0000:01:00.0
version: a2
width: 64 bits
clock: 33MHz
capabilities: pm msi pciexpress bus_master cap_list rom
configuration: driver=nvidia latency=0
resources: irq:142 memory:dc000000-dcffffff memory:b0000000-bfffffff memory:c0000000-c1ffffff ioport:e000(size=128) memory:dd000000-dd07ffff
*-display
description: VGA compatible controller
product: HD Graphics 530
vendor: Intel Corporation
physical id: 2
bus info: pci@0000:00:02.0
version: 06
width: 64 bits
clock: 33MHz
capabilities: pciexpress msi pm vga_controller bus_master cap_list rom
configuration: driver=i915 latency=0
resources: irq:138 memory:db000000-dbffffff memory:70000000-7fffffff ioport:f000(size=64) memory:c0000-dffff
Usando Ubuntu 19.10 e navegador Chrome. Versão 78.0.3904.108 (versão oficial) (64 bits).
Compartilhar a tela inteira funciona perfeitamente.