DRV8860 - Open drain output with 1.4k internal pull-up - How to understand this low value
Why for example they would not put a high value (&quot;weak&quot;) pull-up there
instead?

Well, the main use of DOUT is when daisy-chaining several DRV8860 devices: -

And, when used like the above, a relatively low value for the internal pull-up resistor is needed to ensure that data can be transferred daisy-chain fashion at reasonable speeds. Of course, TI could have used a much higher value internal resistor and then, when daisy-chaining, suggest that an external pull-up is used.
But, it's probably a committee/marketing thing where votes were taken around a table and the outcome was a compromise. If you really do need feedback of the serial data you have dropped into the chip, then you would be advised to use a potential divider from DOUT to match the Vcc of your host.