Can you elaborate on what makes them look strange?
There are a number of official coins: the silver and gold 25th anniversary coins; the Makyr coin most recently released; and, closest to these, the military promo coins for both 2016 and Eternal. The thing that makes me question if this isn't fanmade is that the enamel coin here is, to me, higher quality than the official D:E coin released (pictured below).
I don't have the 2016 coin yet, but it's completely different in design. (Image courtesy of Snoopy101x on imgur)
Here are the links to the coins currently available.
DOOM I: https://www.ebay.com/itm/Doom-Collectors-Challenge-Coin/293753593757?hash=item4465141f9d:g:VIkAAOSwGyteqIR9
DOOM II: https://www.ebay.com/itm/Doom-II-Collectors-Challenge-Coin/293753593094?hash=item4465141d06:g:eCUAAOSws6ReqIVS
DOOM ETERNAL: https://www.ebay.com/itm/Doom-Eternal-Collectors-Challenge-Coin/293753592594?hash=item4465141b12:g:O1AAAOSw8Rte~Ofr
I purchased the D:E coin from a different seller and that listing is no longer up, but I should note that both sellers are from the Clearwater, FL, area. If it is fan-made, I think it's likely that they were produced - or at least ordered - by someone there.