Some (mostly gog.com-based and linux friendly) suggestions:

Astrologaster – essentially an interactive visual novel about a Tudor doctor who diagnoses people by looking at the stars. Cracking (tudor choir music) tunes. https://www.gog.com/en/game/astrologaster

The Talos Principle – a puzzle-em-up which uses the FPS perspective but entirely for solving rather hard logic puzzles and with little reference to war, but a surprisingly engrossing plot – https://www.gog.com/game/the_talos_principle_gold_edition

To the Moon – another essentially visual novel, but in the style of a 16 bit RPG – https://www.gog.com/game/to_the_moon. Also, A Bird Story, its sequel: https://www.gog.com/en/game/a_bird_story

A Short Hike – a very cute, adventure/exploration game with no combat at all – https://www.gog.com/game/a_short_hike

Slipways – a strategy game that scratches the RTS itch, but isn't RT and has no combat – https://www.gog.com/game/slipways

Superliminal – a puzzle game entirely based on perspective, again with an excellent (if creepy) plot – https://www.gog.com/game/superliminal

Gorogoa – an absolutely beautiful visual puzzle game with a charming, graphically told plot – https://www.gog.com/game/gorogoa

Obduction – an excellent Myst-like puzzle experience that tells a lot with no combat – https://www.gog.com/game/Obduction

The Witness – a really surprisingly varied difficulty, excellent, puzzle game that has lots of hidden secrets – https://www.gog.com/en/game/the_witness

An "honourable mention" would be Caesar III and its open-source engines (Julius and Augustus) which, whilst not being combat-free, is an entirely combat-optional town-building RTS game where the economic-only missions are far, far harder than those where you defeat a military enemy. This is arguably true of Roman society, as it happens…