Actually, carrying the ball was a commonplace in many of the regional variants of the sport played throughout England prior to the attempts of the public schools (private schools in U.S. parlance) to establish one set of national rules, which in reality failed and gave rise to the officially defined, separate sports of rugby football and association football.
Ellis gets credit only for doing at a public school in what was supposed to be an association game that which was done commonly elsewhere in England.
This is also why American rules football, Australian rules football and (to a lesser extent) Canadian rules football all vary so widely: they were all outgrowths of what we might call the primitive football variants played throughout the British Isles, and either missed the attempts of the public schools standardisation entirely, or diverged at early enough stages from the association or rugby rules standardisation process that their common pedigree is no longer clear.
But, bottom line, there was no single game played today which can claim to be the original “authentic” football.