Here's a in depth video about the BRN-180 comparing it against the original AR-180 from Brownells official channel.
The guide rods, rod springs, bolt and bolt carrier are all shorter then the original 180's and presumably the WK's , as they are shortened to accommodate being an AR-15 upper, so no parts commonality there. As noted upthread, the charging handle has an indexing key piece that would need to be milled out of the WK's bolt carrier group in order for it to work with the WK. The hand guard and its mounting bracket are both proprietary, so the WK is superior in that respect. The piston and mounting parts look like they may work with the WK, as they were directly copied from the AR-180. Of particular interest is they've reproduced the original AR-180 flash hider, and it apparently shoots quite nice. Wolverine may want to bring that in to sell to WK owners, as its a standard AR-15 threaded flash hider.
In the comments section of the Youtube video, I see continued complaints that this is not a true AR-180 reproduction, with people noting an American company has made AR-180 lowers. Well, so has Wolverine and Kodiak
It looks like Brownell's partnered with PWS to develop and manufacture the BRN-180. If Wolverine and Kodiak could produce a retro-looking handguard, maybe they could partner with Brownells to sell the WK as an AR-180 Retro?