I think spoke length is measured to inside of the elbow, which is different from above by only 1mm typically.
Your picture looks like 2 cross to me, large hubs are often 1 cross.
You can see the difference if you play around with the spoke calculator mentioned above. If you put in the relevant data you should be able to confirm your 200mm spoke length. This is a good start for understanding what is needed to re-lace a wheel. Ideally a spoke should be just shy of protruding from the nipple, (not always possible).
At least with a large hub you won't have to remove the cassette (or freewheel) to replace spokes. Maybe you need to keep a spare spoke handy in case of further problems? One broken spoke can stress the next and so on. Check spoke tension without tools by squeezing two together by hand between cross and rim and comparing around the rim, and comparing with a known good rim with similar pattern etc. You're going to need to do this when you replace your broken spokes. Remember that spoke tension on a dished wheel differs from drive side to non-drive side slightly, (or disc side to non-disc side at the front, possibly).
If you do re-lace take lots of pics and allow quite a bit of time, if it's your first. Read Sheldon Brown's guide (as you progress), and allow for the fact that electric motor hubs are sometimes laced with spokes leaving on one side of spoking flange instead of alternating, witness marks on the hub will give a clue after disassembly. These details can be seen on the spoke calc graphics quite well, I think. My opinion is wheel building whilst a challenge can be quite rewarding.
Are 2mm = 14g spokes thick enough, for these hubs? Any opinions, either way, anybody?