No, it should not run afoul of the match rules, this is a double-round-robin event. The validation report will (properly) indicate that players faced opponents more than once, but that is not an error or warning, just an advisory message.
However, depending on how many players there are, you could run into some problems getting the event uploaded. WinTD and SwisSys used to have limits of 14 rounds, so if there are more than 8 players you could have some problems creating and uploading it. (As far as I know, WinTD still has a 14 round limit but I’ve recently been told by Thad Suits that the latest version of SwisSys now supports events up to 20 rounds, but I do not have a copy of it to test whether those events upload correctly.)
One way around this is to create two pairing #s for each player, like this:
1 (P1)
2 (P2)
3 (P3)
4 (P4)
5 (P1)
6 (P2)
7 (P3)
8 (P4)
Pairing #'s 1-4 play each other and pairing #'s 5-8 play each other. Because we aggregate all games under each USCF ID before rating them, this will properly rate all of P1’s games (as pairing #1 and 5) together, etc.
You could also use the online editing form to create the event, it will handle events up to 32 rounds. (There’s no particular reason for the number 32, it was chosen as an arbitrary upper bound. So far the largest event we’ve rated under the current programming was a 24 round event.)
By extension you could do a triple or quadruple round robin and it would still not fall under the match rules. However, if a player faces the same opponent more than twice in an event, that player is not eligible for bonus points under the ratings formula.
There’s probably a point at which the office would be inclined to look at an event more closely to see whether it falls within the spirit of the match rule limitations, such as a four player event where each player plays the others 6 times each, but that would fall under the ED’s discretionary authority to protect the integrity of the rating system.