As far as I know, yes. When I converted my snowflake wheels I definitely had to change the axles. The stock axles for loose bearings were 11mm, and the new sealed bearings required a 12mm axle. The bearings you linked are 12mm ID too.
It looks like you're converting from spokes; I haven't done that, but a quick check with a set of calipers would confirm the size of the axles your bike currently has.