If the existing stepper motor driver board takes step/direction signals then it's straightforward to get mach3/emc to work and you wont need the big board. However that's not immediately obvious from the photos. I doubt they'll be good drivers anyway - though that's not a problem if you're working within the original specification.
You could get 3 new stepper drivers and just forget the rest of it, except maybe the spindle board - looks like there's some writing/numbers you could look up to see if there's any info on that? Look what model number and/or ratings are printed on the stepper motors then so long as the datasheet is available we can work out which drivers will be suitable. Also check what voltage and VA (or approx dimensions to guess VA) the toroidal transformer is as you may be able to reuse that.