That's an interesting stat. Missouri was a very important front in 1861 and looking at it like this makes it much more apparent. Did Mr. Wolk provide his basis? Qualitatively it looks about right.
I think 45% is not too far off for casualties if one includes prisoners. Lexington has a significant impact in this regard. Without captures at Lexington, MO and Hatteras Inlet, NC the Missouri fraction is a few percent lower. Interestingly, the NPS/ABPP/CWSAC summaries seem to have a low value for Lexington (only about half of Mulligan's command.)
In order, the largest casualty totals (K/W/C) for 1861 appear to have been: 1st Manassas, VA; Wilson's Creek, MO; Lexington, MO; and Belmont, MO. (Lexington might be #2 on that list rather than #3, but I've not looked at how it should properly be quantified--and it falls far lower if captures are omitted.)
It looks like casualties in 1861 were somewhere on the order of 16-20,000. A few months later the battle and fall of Fort Donelson alone would be in the same range (primarily surrendered) while Shiloh's butcher bill would swamp the total 1861 casualties in terms of killed and wounded.