I've been thinking about this, and I'm fairly happy with where I've ended up.
Apologies in advance for the inevitable wall of text to follow, but here are my thoughts.
Firstly, it's essentially all about Sport mode.
It begins: "Keeping things fair"
Then: "a world first" blah, blah, blah, "FIA" blah,blah,blah, "Charlie Whiting" blah, blah, blah, "racing integrity" blah, blah, blah.
It continues: "In order to ensure fair racing for all, GT Sport will require an internet connection for the majority of functionality. This connectivity requirement is to ensure that progress, car availability and driver ratings are properly maintained at all times."
Progress, car availability and driver ratings are all linked, and really only relevant in Sport mode.
As you progress through the game you win cars, therefore the game will know you have an appropriate car for the race it is matching you to.
You also earn experience points in both Campaign and Arcade modes which go towards your Driver Level.
Driver Level wasn't seen in the beta, but it's the third metric (along with Sportsmanship Rating and Driver Rating) that is used for the match-making system.
And then there are the Achievements such as Distance Driven, Time Driven, Clean Races, etc which also offer rewards as you progress through the game.
Yet another indicator for the game to know what cars you would have won, your Driver Level, etc.
So again, it's all about fairness of racing in Sport mode, and helping the match making system do it's work.
As for the other strange wording of that section of the blog post, I have a few thoughts.
"Single player on select tracks".
I note that even though some tracks are available in Circuit Experience they are not available in Arcade Single Player.
So perhaps it's as simple as not all tracks are available there.
And therefore "select" Single player tracks.
"portions of Arcade Mode"
Clearly leaderboards (and perhaps ghosts) require internet connection.
But there is a Multiplayer Battle option.
At first I took that as LAN gaming.
But the sub-menu here are "Create Session", "Search Session", and "Friend's Session".
So perhaps it is a pre-organised LAN option using the internet as I first suspected.
Or it could even be you and a few mates racing against AI cars in an online environment.
Eitherway, it's obviously a part of Arcade that uses internet connection.
Hence "portions".
"Limited two-player split screen".
Don't know with this one.
Perhaps again it's limited due to the track options available.
Or perhaps they were trying to seperate it from Multiplayer Battle by suggesting the "limited to 2 players" mode.
And after saying all that I'll add one last thing.
I see absolutely no reason why not being connected to the internet means you don't win credits and therefore cannot buy cars.
I see absolutely no reason to assume the Campaign, Livery Editor, etc. requires internet connection, simply because it wasn't specifically named in that particular sentence, which was about PS Plus anyway.
And mentioning that, I see no reason why PS Plus is required for anything other than online multiplayer gaming.