Are you running these games in VGA mode? I'd first suspect that your TFT cannot display a 70Hz signal. Many (most?) VGA games are 70Hz, Battle Chess is 70Hz to my knowledge.

Do other games work?

Hi, what hardware specs? Is it a vintage PC? ISA VGA card or PCI VGA card?
Because, ISA VGA cards had DIP switchs to define the monitor type (IBM, NEC multisync, SVGA etc).
These switch settings defined what timings the VGA card would produce.
A TFT monitor isn't multi-sync, for example. It can only use a set of standard frequencies.

Hi,

If you suspect that the problem is the TFT monitors not supporting the VGA card frequency you can check the timings from these lists:
https://martin.hinner.info/vga/timing.html
The second table lists the standard VGA and VESA BIOS modes, and yes 70Hz is one of the more commonly used Vertical Frequencies.
Note: For those games which directly program the CRTC you might find odd frequencies.
Note2: If you actually program VESA, newer cards does not need to support the standard VESA mode numbers as they have made the fixed mode numbers obsolete in a newer version of the standard(VBE 2.0), most VESA cards produced even after they have been declared obsolete still support them for backwards compatibility though, but the official way to find a mode after VBE 2.0 is that you need to call the Video Interrupt(10h) with VESA functions(AH=4FH) with function number AL=00h to get the list of modes, then ask each modes properties with VESA function AL=01h, until you find the most suitable mode.

But how common is a monitor with native VGA input but that can't handle 720x400 @ 70 Hz and other such classical VGA modes? Are we really that far removed from VGA text mode that such a monitor is even saleable?