Successful Rome's engineering and infrastructure

Absolutely yes. A basic premise of my TL is steady contact since Principate/Han times creates a virtuous imitation/competition dynamic between Rome and China that helps both empires overcome their flaws and evolve into industrialized superpowers. India eventually unites and joins the game because frankly it is the only way the Indians can avoid colonization by the imperialist Romans past a point. E.g. the example of China inspires Rome to create an extensive professional civil service to help checking the problem of military anarchy (other reforms also deal with this). To be fair, OTL Rome eventually did something similar in Byzantium, so it had homegrown potential for this on its own, but here it goes even further thanks to foreign example, and also because Rome suffers no decline and the Germanic, Slav, and Arab peoples are conquered and turned into a resource long before they can become a threat. Much the same way, steady contact with Rome inspires China to shake out Confucian stasis and complacence, and become just as interested in expansion, trade, and progress as Roman Europe. Because of geography, its expansion unfolds in Central Asia, East Asia, Southeast Asia, Oceania, and the western coast of the Americas. Korea, Japan, and Indochina are conquered and absorbed by an expanding China, and there is no 'Divine Wind' to save Japan ITTL, so in due time Seoul, Kyoto, Saigon, and Bangkok become as Chinese as Beijing, Nanjing, or Canton.

Of course, geopolitical factors make Central Asia, Siberia, the Malay Archipelago, and Australasia potential contested lands between Rome, China, and India, and the outcome may vary depending on military, diplomatic, and colonial variables. My best guess is borders and spheres of influence in these areas may shift back and forth considerably over time in these areas. Geography gives a vast colonization advantage in the Americas to Rome east of the Great Divide and to China west of it, so I expect that becomes the final demarcation line between the two empires in the Americas, give or take a few adjustments. The Neolithic or Bronze Age Pre-Columbian civilizations simply don't have a snowball's chance in Hell to resist Roman or Chinese colonization given the massive technological, organization, and demographic (even more so after disease does its grim job) gap with the Early Modern Eurasian empires. The Romans acknowledge the Chinese and the Indians as worthy equals with a lot of interesting ideas in terms of power and sophistication and are fine with making the Amerindians dark-skinned citizens of the empire, but have no respect for weaker and backward 'barbarian' cultures. Moreover, the enthusiasm for human sacrifice of several Pre-Columbian cultures in all likelihood freaks out the Romans in thinking they are doing the world a favor by wiping them out.

Climate and disease prevent the Romans from doing any extensive penetration in the western half of Sub-Saharan Africa for most of their history, so they make themselves content with some trade and indirect influence projecting from coastal outposts or the other side of the Sahara, and this quite possibly builds up a lasting precedent. Thanks to the Suez Canal and their control of the Red Sea and the Persian Gulf they also have no use for circumnavigation of Africa as a route to reach Asia, so the western side of Africa is marginal to their global interests. A possible exception for the same reasons may be East Africa and Southern Africa, since these regions are much more favorable to extensive European settlement than the rest of the continent, and the eastern coast of Africa is easy to reach from Roman lands, so Roman colonization of the area may well occur if the Romans are not too busy and/or sated with colonization elsewhere. Geography also makes the Asian empires not likely to get interested in colonization of Africa, again with the possible exception of India and eastern-southern Africa. So Sub-Saharan Africa is the most likely region of this world to see the rise of important polities that survive assimilation or utter domination by the Eurasian superpowers, although any African polity shall always be a midget to them. The other area of the world where indipendent polities are likely to arise and survive as buffer states is the friction zones between the spheres of influence of the empires, especially if they are of low value.

Of course, Rome and China (and after unification, India) remain vulnerable to dynastic cycles, although past a point evolution into early modernity and industrialization snuffs them out. My TL's calculations expect Rome to achieve the Renaissance stage by the turn of the first millennium, and remain as dynamic as OTL Europe. China achieves pretty much the same level of dynamism in its own sphere. So we may expect TTL Eurasian empires and their colonies achieve industrialization by the half of the second millennium, and the Information Age by its last quarter. China and Rome are also expected to develop gunpowder on schedule by the beginning of the second millennium, which marks the point the steppe nomads turn from perennial nuisance and occasional serious threat into insignificant and powerless target for conquest. Even before that, the better shape of Rome and China means they suffer less damage from nomad breakouts (e.g. Rome pushes back the equivalent of the Huns with some effort).