Is there any short summary of John Rowe's theory of horizons about the Incas?

You might want to go to the source of this theory as presented in the article Absolute Chronology in the Andean Area American Antiquity, Vol. 10, No. 3 (Jan., 1945), pp. 265-284.

This only forms the basis for that theory as it was later developed. A first priming definition of terminology:

The following eras of ancient Peru (1800 BC-AD 1534) have been defined by archaeologists using an alternation of so-called “periods” and “horizons” which end with the arrival of the Europeans.

The term “Periods” indicates a timeframe in which independent ceramic and art styles were widespread across the region. The term “Horizons” defines, in contrast, periods in which specific cultural traditions managed to unify the whole region.
_{Timeline of the Andean Cultures of South America}

In other words, periods are times of divergence, evidenced by a multitude of finds with stylistic variations. Horizons are times of convergence, evidenced by a multitude of finds with stylistic similarities.

That means that in the Preceramic Period, starting at around 9500 BCE, human presence is evidenced. Human presence = culture, even if a specific name might be missing. But using this very early reference point might be overzealous for tracing the origin of the Incas'.

These terms just defined are of archaeological origin. While we should still keep in mind that:

All dates for the earliest periods are, and always have been, exceedingly unreliable guesswork, and much more exploration is necessary before it will be safe to suppose that we have found the beginnings of the high cultures in the Andean area. (Rowe 1945)

His findings and terminology is explained in more detail in John Howland Rowe: "Stages and Periods in Archaeological Interpretation", Southwestern Journal of Anthropology 18, no. 1 (Spring, 1962): 40-54. DOI

"Origins of the Incas" might be a slightly problematic concept here. The emerging Incas are only found in the very last period (within the terminology here: "horizon"), except for the small Kingdom of Cusco. So this system might be better described as a chronology based on the archaeological record for the region and the Incas' predecessors.

Since you seem to look for a very short summary, the above links give you that:

Preceramic Period

Preceramic Period I (before 9500 B.C.E.): First evidence of human occupation of Peru comes from groups of hunter-gatherers in the highlands of Ayacucho and Ancash. Fluted fishtail projectile points represent the most widespread lithic technology. Important sites include Quebrada Jaguay, Asana and the Cunchiata Rockshelter in the Pucuncho Basin.
Preceramic Period II (9500–8000 B.C.E.): this period is characterized by a widespread biface stone tool technology on the highlands and on the coast. Examples of this tradition are the Chivateros (I) industry and the long and narrow Paijan points. Other important sites are: Ushumachay, Telarmachay, Pachamachay.
Preceramic Period III (8000–6000 B.C.E.): From this period, it is possible to recognize different cultural tradition, such as the Northwestern Tradition, where the site of Nanchoc dates to ca 6000 BC, the Paijan Tradition, the Central Andean Tradition, whose widespread lithic tradition has been found in many cave sites, such as the famous Lauricocha (I) and Guitarrero caves, and, finally, the Atacama Maritime Tradition, at the border between Peru and Chile, where the Chinchorro culture developed about 7000 years ago. Other important sites are: Arenal, Amotope, Chivateros (II).
Preceramic Period IV (6000–4200 B.C.E.): The hunting, fishing and foraging traditions developed during the previous periods continue. However, toward the end of this period a climatic change allows for early plant cultivation. Important sites are: Lauricocha (II), Ambo, Siches.
Preceramic Period V (4200–2500 B.C.E.): This period corresponds to a relative stabilization of the sea level along with warmer temperatures, especially after 3000 BC. Increase in domesticated plants: squashes, chili peppers, beans, guavas and, most of all, cotton. Important sites are Lauricocha (III), Honda.
Preceramic Period VI (2500–1800 B.C.E.): The last of the Preceramic periods is characterized by the emergence of monumental architecture, population increase, and widespread production of textiles. Different cultural traditions are recognizable: in the highlands, the Kotosh tradition, with the sites of Kotosh, La Galgada, Huaricoto, and along the coast, the monumental sites of Caral Supe / Norte Chico tradition, including Caral, Aspero, Huaca Prieta, El Paraiso, La Paloma, Bandurria, Las Haldas, Piedra Parada.

Initial through Late Horizon

Initial Period (1800 – 900 B.C.E.): This period is marked by the appearance of pottery. New sites emerge along the coastal valleys, exploiting the rivers for cultivation. Important sites of this period are Caballo Muerto, in the Moche valley, Cerro Sechin and Sechin Alto in the Casma valley; La Florida, in the Rimac valley; Cardal, in the Lurin valley; and Chiripa, in the Titicaca basin.

Early Horizon (900 – 200 B.C.E.): The Early Horizon sees the apogee of Chavin de Huantar in the northern highland of Peru and the successive widespread of the Chavin culture and its artistic motifs. In the South, other important sites are Pukara, and the famous coastal necropolis of Paracas.

Early Intermediate Period (200 B.C.E. –600 C.E.): The Chavin influence wanes by 200 BC and the Early Intermediate period sees the emergence of local traditions like the Moche, and Gallinazo in the north coast, the Lima culture, in the central coast, and Nazca, in the south coast. In the northern highlands, the Marcahuamachuco and Recuay traditions arose. Huarpa tradition flourished in the Ayacucho basin, and in the southern highlands, Tiwanaku arose in the Titicaca basin.

The Middle Horizon (600–1000 C.E.): This period is characterized by climatic and environmental changes in the Andean region, brought about by cycles of droughts and El Niño phenomenon. The Moche culture of the north underwent a radical reorganization, with the move of its capital farther north and inland. In the center and south, the Wari society in the highland and Tiwanaku in the Titicaca basin expanded their dominion and cultural traits to the whole region: Wari toward north and Tiwanaku toward the southern zones.

The Late Intermediate Period (1000–1476 C.E.): This period is signified by a return to independent polities governing different areas of the region. In the north coast, the Chimú society with its huge capital Chan Chan. Still on the coast the Chancay, Chincha, Ica and Chiribaya. In the highland regions the Chachapoya culture arose in the north. Other important cultural traditions are the Wanka, who opposed a fierce resistance to the first expansion of the Inca.

Late Horizon (1476–1534 C.E.): This period spans from the emergence of the Inca empire, with the expansion of their dominion outside the Cuzco region until the arrival of the Europeans. Among important Inca sites are Cuzco, Machu Picchu, Ollantaytambo.