As far as I know, Venture Lighting was known for developing metal halide lamps that had wattages that were not seen on other metal halide lamp manufacturers such as 575w lamps, 200w lamps, 125w lamps 300w lamps, and 875w lamps. Why did Venture lighting manufacture metal halide lamps with such non-standard wattages?

Thez used special ballasts, which modulated the lamp power on a way to compensate for efficacy loss as the lamp wears out.
The system was set so, the light output corresponded to the mean (or minimum - not sure anymore, it is a few years since I read the articles) lumen output of an equivalent standard wattage lamp. Because when the lamp is new and over majority on its life the efficacy is higher, the average power input over the lamp life in this system is lower than the corresponding equivalent, hence the different ratings ("200W" iso 250W, "300W" iso 400W, etc).

That way the real electrical power (assume 250W equivalent) started at less than 200W, then gradually rose till 250W at the rated EOL, so the average over the lifetime was the 200W corresponding to the formal rating.

Because they could...

Yep. A way of locking the customer into only being able to buy replacements from a strictly controlled source, at a price... 

This same topic was covered very recently in the image gallery, see https://www.lighting-gallery.net/gallery/displayimage.php?album=6415&pos=2&pid=228332

I missed that, thanks James 

So the the reply from James in the gallery was mostly a very polite way to describe a consumer locking in "Of course we do this for your benefits". Interesting what scale of performance gains was promised, probably in single percents range, which is usually buried in the other noise like inflation and energy price fluctuation?

We avoid this like plague at work with electronics. Even if there is a magic chip that solves the problem more efficiently, there is usually too much risk to have a single source, manufacturer can hike the price, go out of biz, there may be a global shortage like recently etc. Though our economics may be different to the HID lamp area, energy price usually do not matter, but the development is pricey, equipment is sold and the money is spent at a single time, but the the reliability and reputation counts etc...

Are the 875w lamps CMH? I wonder what their outer envelope looks like