Is this the first time that two different companies will be allowed to sell full box (i.e. non-travel) versions of home games?
No. Back in 2016, I assumed that Cardinal Industries, which was bought by Spin Master, became the new licensee to Family Feud games when their Disney Edition FF was promoted on their prime-time Celebrity series. Though in early 2017, Endless Games released their sixth edition game and within six months. their 40th Anniversary edition! A major difference Cardinal/Spin Master's games featured all regular and Fast Money round questions on cards, and two different pads of pre-printed paper for use during games, regular and Fast Money rounds. EG had all questions/answers (both regular and FM) printed in a booklet, and a dry erase folding board to write on! Also EG had Steve Harvey's photo on box cover, whereas Cardinal/SM did not.
By 2019, EG no longer had any licensing right to FF, and Cardinal/SM/Imagination Gaming began using the dry erase board concept, as well as featuring Harvey's photo on box cover!
I think, by my own observation, similar games just don't have to be designed 100% the exact same as I just described earlier. I could be wrong, but I am not a lawyer (IANAL), and never heard of any legal troubles during that time.
With the Pressman edition looking the same as we know it to be like, the Just Play version will have a differently designed puzzle board, a different wheel, and, of course, Ryan Seacrest's photo on the box, according to early viewing. Of course, back in 1999, Hasbro's prototype boxes for WOF, J! and HS home games featured photos of Vanna, Alex Trebek, and Tom Bergeron/Whoopi Goldberg respectively (the actual products DID NOT!)