Plus Vietnam is able to differentiate itself from the rest of SE Asia by having closer ties to China and not be as similar as the Khmer.
This. Southeast Asia is a geographic territory, but Vietnam is an expansionist Chinese state (just like its contemporaries, Wu, Min, Wuyue, Jingnan, Former Shu, Later Liang and Dai Viet...modern Southern Han) the dynasty of which was the only one successful at not being rolled over by the emerging Song state which would end up establishing Song dynasty. And so you get a southern Chinese state taking on some hints of their neighbors, but still being very Sinitic. Ho Chi Minh is my favorite example. He got his education because he was the son of a mandarin. While he went on to become a revolutionary, his brother became a feng shui geomancer. The stripes on the flag of South Vietnam are a Daoist trigram just like the ones found on the flag of modern South Korea.
All of their literature, records and everyday signs are in Classical Chinese, rest of SE Asia uses Sanskrit or some derivatives thereof.
They built pagodas, rest of SE Asia built stupas.
They were staunchly Confucian, the rest of SE Asia operated on Indic philosophical traditions.
Religiously they were Zen Buddhists, rest of SE Asia was either Hinduist, Theravada Buddhist, or even Muslim.
They operated with clear borders guarded with walls and soldiers, rest of SE Asia used the Mandala system.
They used the Han-Barbarian distinction in governance and thus actively resettled and assimilated the barbarians under their rule (most famously Champas), rest of SE Asia did not require homogenosity of its empires (it's also the reason Myanmar/Burma has active ethnic cleansing running to this day, Thailand has to continually battle separatist movements on most of its modern territory).
To get a government position you had to pass the Imperial Examination, in SE Asia it was always? (help me here, folks) the aristocracy selecting people for positions.
Of course, the syncretisms are there, but they are on top of two fairly different and distinct cultural bases.
For instance, Sinitic weapons and the Lunisolar Zodiac calendar (+ Chinese New Year celebrations) are used even in Thailand and Cambodia.
On the other hand, Vietnam did incorporate stuff from both their neighbors and conquered subjects, like the strong elephant-status symbolism.