if you view Christ as suffering a prescribed amount of wrath and punishment for each and every sin committed by each man being discussed with nothing else going on as far as the propitiation for sin. In other words, a sin, atoned for is cancelled regardless of any other interaction between God and the man.
When the Name for Him being The Savior was mentioned, in Matthew 1:21, then Jesus' Mission is described as, "He shall save His people from their sins", with "His people" and "their sins", both being indicated as expressing them as being specific " people" = "His" and "sins" = "their".
When Jesus describes How He was going to accomplish the salvation of His people from their sins, He says, "I give My Life a Ransom for many", again defining a restriction in contrast to Him having given His Life a Ransom for every member of the human race, by stating that He was going to die for "many".
When Jesus spoke directly regarding the subject of who it was that He was to die for, Jesus said, "I give My Life for the sheep".
And what I would like to have asked Owen, respectfully, was how he dealt with the argument for limited atonement without going into hyper-Calvinism and also how would his argument mesh with his view of a real and universal offer of the gospel to everyone who hears it.
The Gospel is Commanded to be preached by Jesus Christ, in the form of, "Repent and believe the Gospel", meaning the Gospel Message that Jesus died, as the result of taking upon Himself the sin of individuals that caused His death, which are the sins the saved soul are Commanded to Repent of, then that Jesus was buried and buried their sins away, and where we know God Accepted Jesus' Payment for their sins, because He Raised Him from the dead.
The God Who Elected some to salvation, also Elected the Means by which He would use The Gospel Message preached, with The Holy Spirit making the Awareness of the Application of the salvation Jesus had Made Satisfaction for, in The New Birth, when that saved soul is Granted Repentance, to now take sides with God against themselves, and at the same time, God Gives that saved soul the Inward Means, by which God Gives them a Spiritual Ability when He Grants them Faith, to grasp hold of a Spirit Enabled understanding that when Jesus died, He died for them, specifically.
Hyper-Calvanism is an entirely disobedient refusal to preach the Gospel, and proves to be the evidence that any claims they may make concerning their belief in God being Sovereign are simply bogus, since they do not do what God Commands them to do and, in fact, their failure to obey God Command to preach the Gospel is also indicative of an actual hatred of the Gospel being demonstrated and expressed.
Jesus Commanded that The Gospel be preached, which always implies that since it was the sins of individuals which Brought about His death on the cross, that they must Repent of those sins, which they are Shown by The Holy Spirit that they were Guilty of, and have Offended God by breaking His Law, which were what Jesus died for.
I don't worry too much about what a man says and don't know how specific to the wording, "his view of a real and universal offer of the gospel to everyone who hears it", is, as far as whether that was something he would say just like that, but I know Jesus Commanded The Gospel to be preached Outwardly, Commanding all individual sinners to Repent and Believe Jesus died for their sins, to which The Holy Spirit Bears Witness to the ones God Gave Jesus to save. Then, while the rest are Commanded to Repent and Believe, they do not, because they love darkness rather than the Light, and God Leaves them right their where He Found them, i.e., in their sins.
So, the words, "offer of the Gospel", is not a concept that I see having anything to do with Jesus' Command to preach the Gospel, for sinners to Repent and Believe it.
The Gospel is a real and universal Command to all, which is either Used by The Holy Spirit by Enabling the lost soul to have ears to Hear that it is Intended for them, personally, when God Quickens them from the dead, by it, or allows the lost sinner to remain in their deaf and blind, Naturally Born Spiritually dead State.