The country was known and sparsely settled as far north as the Orange River, but beyond there was a great region which had never been penetrated save by some daring hunter or adventurous pioneer. It chanced—if there be indeed such an element as chance in the graver affairs of man—that a Zulu conqueror had swept over this land and left it untenanted, save by the dwarf bushmen, the hideous aborigines, lowest of the human race. There were fine grazing and good soil for the emigrants. They traveled in small detached parties, but their total numbers were considerable, from six to ten thousand according to their historian, or nearly a quarter of the whole population of the colony. Some of the early bands perished miserably. A large number made a trysting-place at a high peak to the east of Bloemfontein in what was lately the Orange Free State. One party of the emigrants was cut off by the formidable Matabeli, a branch of the great Zulu nation. The survivors declared war upon them, and showed in this, their first campaign, the extraordinary ingenuity in adapting their tactics to their adversary which has been their greatest military characteristic. The commando which rode out to do battle with the Matabeli numbered, it is said, a hundred and thirty-five farmers. Their adversaries were twelve thousand spearmen. They met at the Marico River, near Mafeking. The Boers combined the use of their horses and of their rifles so cleverly that they slaughtered a third of their antagonists without any loss to themselves. Their tactics were to gallop up within range of the enemy, to fire a volley, and then to ride away again before the spearmen could reach them. When the savages pursued the Boers fled. When the pursuit halted the Boers halted and the rifle fire began anew. The strategy was simple but most effective. When one remembers how often since then our own horsemen have been pitted against savages in all parts of the world, one deplores that ignorance of all military traditions save our own which is characteristic of our service.
Edit. Reposting link.
I don't know which part you're asking about: the battle, the setting, or the numbers.
Doyle, who is an arch-imperialist (and very much so in the SA War), is speaking here of the so-called mfecane and the wars that accompanied the Boer treks (or the so-called "Great Trek") in the late 1830s and early 1840s. Historians since the 1980s have dismantled this model (also known as the part of the 'myth of the empty land' that conveniently laid open the entire interior for the taking by settlers). The highveld was always pretty sparsely populated, and although many states did centralize in the face of heavier raiding from Zulu parties and those moving in their turn (like Mzilikazi's amaKhumalo 'Ndebele' or 'Matibili' to Doyle) the idea that millions were lost has no evidence. Norman Etherington's work on the Caledon Valley case, and some of my own further north, has really continued to destroy this myth. So there's a kernel of truth, but Doyle is laying out the settler claim to the right to the land there, which is something the British gladly inherited from the Boers (and upheld for them too).
The point about early trekkers with small parties being lost is sometimes true; the party of Louis Tregardt came just after one such group, though most of them would perish to illness in the far north and far east, not hostile action. The case of the battles against Mzilikazi is correct, but there too Doyle leaves some things out. For example, the trekkers were allied with the gun-wielding horsemen of the Tshidi baRolong, who needed allies just as the trekkers did. These kinds of arrangements were fairly common. The defeat of Mzilikazi came after that king had earlier defeated other groups and absorbed them into his moving state. Robert Moffat's Missionary Labours in South Africa talks about Mzilikazi, whom he visited, at some length in this era, if you want a fair sense of what Mzilikazi's state and society were like and stay aware of Moffat's own bias.
The battles--two of them, really, one near the middle Vaal known as Vegkop where allies weren't key, and the one near Marico (Pilanesberg) where they were, but it was inconclusive--served as the basis for claiming land by right of conquest over even the trekkers' own allies. I think Doyle may be conflating the confrontations, and thus inflating Ndebele numbers while depressing Boer ones to tell a story. Timothy Stapleton gets more into this in his 2013 three-volume Military History of Africa (2:225-226). Stapleton's a South Africanist by training so he's aware of the bigger historiography, but doesn't belabor it. Some details are a bit off too; Mzilikazi did call himself umZulu, but his relationship with Dingane and the other Zulu clans was loose. The clan was amaKhumalo, and they became known as amaNdebele (from the Sotho-Tswana word for Nguni-group language speakers) before taking on the label when Mzilikazi then relocated north into what is today Zimbabwe. As for tactics, it's hard to know where those recountings came from. If you look at G. M. Theal's many-volume histories of South Africa, you may find recountings of these fights, and it's those which Doyle may have thrown together. The trek parties were, however, very good at multiplying their advantages, preparing positions, making useful friends, and staying supplied, so there were many lopsided encounters of all sizes.
In any case, Doyle during the SA war (63 years after Vegkop!) must always be taken with a big grain of salt, because he's got a clear agenda in time of war, and the jingoes did not have a monopoly because many vocal critics of the conflict for many reasons existed. It was, in many ways, the first truly modern propaganda war in Europe.
I almost failed to mention Doyle's underlying claim: that hostilities of a rather nasty sort existed between Dingane and the trek parties in general. That's absolutely true. His efforts started with coordinated attacks on trek parties near the kingdom, and culminated in the long-celebrated battle of the Ncome (Blood or Bloed) River, 16 Dec 1838, where a well positioned laager under Andries Pretorius devastated the heart of Dingane's army. After that, Dingane did not actively trouble the trekkers, and within another year or so he'd be on the run from his brother Mpande whom the trekkers and many Zulu notables supported in his challenge. Mpande, or Panda to the Boers and British, sometimes had a prickly relationship with Boer leadership but generally remained a friend for the duration of his reign.
Dingane's efforts to wipe the Boer trek parties out before 1839, however, were absolutely real. Lots of other questions always swirl around that, but I don't want to get too far into the weeds because Doyle doesn't mention it in that passage. Still, it fits the same model of the commando as a powerful point application of force, although there too the value of allies (Port Natal traders, other trek parties, and even Africans opposed to Dingane) was downplayed in histories of the era written before the last half century or less. That's always striking, because the Boers did not hide the importance of these many links at the time, but they dimmed in memory when the mythology of the republics and the 'manifest destiny' (to borrow a term) really came of its own with the rise of a more unified Afrikaner nationalism.
(Edit: Hermann Giliomee's 2nd ed. of The Afrikaners ((2009) is a great read for lots of this from the trekker side.)