New Patch for BZ98R hit steam today unknown ETA here, I will assume tomorrow being the most likely:

Patch Notes - The Red Odyssey 24/08/2016!
24 AUGUST - REBELLION
Mission Tuning
CH02 Mission - Stop bug that could cause unlimited spawning of hunters and reduce enemies in the waves to make less difficult at medium and higher difficulties.
CH03 Mission - Fixed howitzers to work as intended and fixed mine field to be effective against player
CH04 Mission - Add an abandoned enemy ship to make the retreat after discovery possible.
CH08 Mission - Adds time to end so final VO completes
CH09 Mission - Reduce difficulty. The longer cover is maintained, the fewer enemies spawned when cover is finally left. Enemies turrets also became single weapon turrets
BD02 Mission - Reduced difficulty.
BD03 Mission - Difficulty tuned, and several object spawning on top of each other issues fixed.
BD04 Mission - Startup issues fixed. Scavenger's shouldn't leave early which made it hard for new players to follow them. Final chase made more survivable while leaving the epic chase feeling intact.
BD06 Mission - Enemy attack waves slightly reduced
General
A number of minor model fixes applied
Fixed error with point lights. Weapon fire shouldn't cause strange reverse shadows anymore.
Chinese Scavenger emissive fixed (strange glow removed)
TRO Music Added to game, and TRO missions play TRO sound files
Fury hybrids no longer describe themselves as scavengers
Black Dog weapon properly rotates only top to shoot now.
CVHAUL adjusted how it holds items so it can't levitate itself
Fixes BD constructor's description text.
Non-playing sounds for several vehicles such as CH Constructor fixed.
Fixed the CVAPC cockpit

The Patch also includes
Mod samples in Edit Mode fixed to be present and useful samples

Steam Community Page detailing the above.

Changelog for Patch 2.2.301 (added 07 April 2017):

Highlights
- Big performance increases on lower end systems.
- Mods in multiplayer!
- Custom campaigns.
- Visible multiplayer locked, full and launched games within the server browser.

Performance
- Massive code clean-up resulting in a performance increase.
- Shader refactoring resulting in a performance increase.
- Terrain shader and vertex format rewritten to dramatically lower the amount of VRAM used by the terrain.
- Shadow system rewritten to use less VRAM while increasing the quality of the shadows. (Ultra setting shadows setting now use less VRAM then Medium shadows did while maintaining the higher fidelity)
- Shadows can now be abled in all graphical settings including being turned off.
- Effects system has been greatly optimised. Much higher framerate during large battles.
- Added Emissive lighting to low quality graphic settings.
- Added PSSM (Parallel Split Shadow Mapping) shadows at High, Very High, and Ultra shadow settings.
- Increased HDR/Bloom effects.
- Improved automatic LOD(Level of Detail) system for extra performance.
- Fixed Jitter on low/medium shadow settings.
- Improved vehicle collision.

Multiplayer
- Ability to password protect your games.
- Multiplayer now uses a custom server and custom low level netcode.
- Locked, launched and full games are now visible within the server browser.
- New icons added for locked and full games.
- You can no longer kick yourself from the game.

Bug Fixes
- Fixed various random crashes.
- Fixed some network connection issues
- Fixed grey lightning on Great Pyramid.
- Fixed lightning colour.
- Fixed AI wandering off map when interrupted by a sub-task while following a path.
- Fixed Io emissive texture.
- Fixed it so the APC cannot die during the cut scene.
- Fixed being able to destroy the Launchpad.
- Fixed a crash during cut scenes.
- Fixed lighting changing during certain cut scenes.
- Fixed Black Dog Scout and NSDF scout cockpit from sliding off screen.
- Fixed units not decloaking when they lose a pilot.
- Fixed objectives on first training mission.
- Fixed cockpit for the Yeti.
- Fixed collision with the rear of Hephestus.
- Fixed Scale of Chinese Command unit.
- Fixed Training Mission 4 now updates objectives as they are completed.
- Fixed mission name not appearing on the mission briefing screen.

Just got an update and it crashes now :-(

Problem signature:
Problem Event Name: BEX
Application Name: Battlezone98Redux.exe
Application Version: 2.2.301.0
Application Timestamp: 58d9d6cc
Fault Module Name: MSVCR120.dll
Fault Module Version: 12.0.21005.1
Fault Module Timestamp: 524f7ce6
Exception Offset: 000a7666
Exception Code: c0000409
Exception Data: 00000007
OS Version: 6.3.9600.2.0.0.256.48
Locale ID: 1033
Additional Information 1: a189
Additional Information 2: a189b3e85b6b03334e7a9f78eaf303ef
Additional Information 3: 1754
Additional Information 4: 1754300e0858ab4a5fa2aefbaf6fdbd8

Make sure you have the Visual Studio C++ redistributables installed. That could be the cause.

It is.
I've had the game working before, and I wasn't uninstalling anything.
Perhaps rather installing a different version of VC++ redist. The question then is, though - which version do I need to have installed. Getting latest 64-bit version from MS site didn't fix the issue.

Still crashes. Can anyone help me at all?
I've reinstalled all VC++ redistributables I could find - nothing works.

P.S. I have noticed there is a file BZOgreLogfile.log created at the start of the game. It has some error.
Last line of that log file:
21:54:48: OGRE EXCEPTION(4:ItemIdentityException): Resource with the name TI_2_DETAIL_ATLAS already exists. in ResourceManager::add at D:\code\ogre\OgreMain\src\OgreResourceManager.cpp (line 168)

I've got it working. Just deleted all game files except saves and re-downloaded.
Apparently the problem had nothing to do with any VC++ redistributables.
Thanks for nothing guys.

P.S. In case you're wondering - I've tried verify&repair before and it didn't change anything.

This board tends to be very quiet. Given that its most active posters own the game on Steam as well, where the community is much more active, we don't tend to check it often because there usually aren't any new posts.

If you have issues in the future, the fastest way to get help is to raise them on the Discord server, which is linked in a thread below.