After 1866, Steinitz played a number of matches with other players. Those matches are considered unofficial World Championships, but what about the tournaments that were held in the period 1866 to 1886. [...] What does H.J.R.Murray have to say about this subject. His 'History of Chess' first appeared in the early years of the official World Championship.
I found a copy of Murray's book on the Internet Archive: Full text of "A History of Chess". It identifies itself as:-
HISTORY OF CHESS H.J.R.MURRAY OXFORD AT THE CLARENDON PRESS 1913
On p.888, Murray wrote,
With the commencement of the era of magazines, tournaments, tourneys, and newspaper columns, I have reached the limit which I have prescribed for myself. I shall only add the. briefest of references to the crowded chess life of the last sixty years.
Before he signed off, Murray had a few paragraphs on the Anderssen era:-
With Anderssen’s triumph in the 1851 Tournament the supremacy of chess passed into German hands, and Germany might claim to be the first chess country of Europe. But circumstances had changed since the time of Philidor, and a claim of this kind, probably never really tenable at any time, had become an absurdity with the general rise in the standard or chess in all countries. The sceptre of chess was henceforward an individual, not a national possession.
That Anderssen’s victory was no chance one was made clear by his success in later Tournaments. Between 1851 and 1878 he took part in twelve Tournaments and his name appeared on the prize list in every one of them, while on seven occasions he won the first prize (London 1851 and 1862, Hamburg 1869, Barmen 1869, Baden 1870, Crefeld 1871, Leipzig 1876). But after 1860 the opinion that the Tournament was not the best way of discovering the strongest player of the day became general, and the match became the recognized test.  It was as a result of his match with Wilhelm Steinitz, in 1866, which he lost by 6 games to 8, that Anderssen’s supremacy is assumed to have come to an end.
From this I took away two main points. The first was a transition for any World Championship (as a concept) from a 'national possession' to an individual possession. The second was in the sentence that I repeat:-
After 1860 the opinion that the Tournament was not the best way of discovering the strongest player of the day became general, and the match became the recognized test.
Murray gave no references to support that statement; note '' is irrelevant to the sentence in question. On what evidence did he conclude that 'the opinion became general'? I'm afraid that might be looking for a needle in a haystack, but a good place to start would be the Early Chess Periodicals (April 2019) that I collected last year.