Your talking about a reverse deathmatch gungame. I've played many many games of gun game, and when i first played this one I was like ohhhh cool...then after like 3 more rounds i began to hate it. In the original type of gungame the time for the "worse players" to catch up was when the "better player" were on nade and knife, and I've always felt that that works best. My favorite type of gungame is turbo gungame with knifepro, in this type you get the next gun immediately upon a kill, and can steal levels from other players by knifiing them thus gaining you a level and losing them one. The only levels you can't skip with a knife kill are nade and .... knife(that sounds weird). Most servers also bump up late joining players levels based on that person's server rank the higher the players rank to worse gun they start with no matter what level the other players are on, but in most cases gungame servers have a much smaller playerbase then an open pub like gc so i'm not sure how that part would work on a gc server. Gungame is good fun, but sometimes its just as frustrating as fun.
Oh and gungame with awps involved in the rotation is lame.