Vietnamese not culturally closer to Korea and Japan than its SEA neighbor might have been an understatement. If you look closer there’s a lot of similarities. Like:
Vietnamese used clothings that resemble kimono in Japan like ao giao lanh(交領衣) before the 19th century.
Vovinam is heavily influenced by Chinese style of Gongfu , and elements of Japanese and Korean systems and it's a Vietnamese marial art.
You can also find Dong Son drums in South Korea. You can also find Joseon works of art in Saigon.
You can also find a Japanese bridge in Hoi An.
You can also find that a Vietnamese Prince called Ly Long Tuong fled Vietnam after his dynasty was destroyed and fled to Korea where he was welcomed with open arms and where he settled and created one large strand of the Korean surname "Lee".
You can also find that Syngman Rhee claimed Vietnamese descent.
You can also find that a Vietnamese princess was married to a Japanese trader called Araki Shutaro. You can also find Vietnamese ceramics in Kyushu.
You can also find ancient Chinese Bronze Artefacts in Central Vietnam. You can also find that the Vietnamese traders had close relations with Okinawan kingdoms.
You can find that Cantonese and Vietnamese pirates worked together and were seen as the same people by inland Chinese people.
You can find that no other dynasties have sent more emissaries and diplomats to Chinese dynastic courts than those of Vietnam and Korea, and the diplomats from Korea and Vietnam meets each other and has a very good relationship, even to use Classical Chinese poems to write about each other.
You can find that Trieu Da and Ly Nam De who both came from China were the first emperors of Vietnam after the Hung Vuong and An Duong Vuong. The same happened in Japan where people from continental China migrated to the Japanese islands in ancient times to mix with the local native ancient Japanese populations of the time, though in this case there was no conquest involved.
More recently, South and North Korea took an active role during the Vietnam war, North Korea sent a fighter squadron to North Vietnam to back up the North Vietnamese while the South Korea sent it troops to stop the communist and allied with the U.S. The number of troops from South Korea was much greater than those from Australia and New Zealand , and second only to the U.S. military force .
After the Vietnam War, the Korean left behind thousands of children of mixed Korean and Vietnamese descent and was accused of war atrocities.
Kango(Sino-Japanese) vs Han Viet(Sino-Vietnamese)
公安(kōan) công an
蛍雪(keisetsu) cảnh sát
困難(konnan) khốn nạn /khốn khổ
結婚(ketsukon) kết hôn
宇宙(uchū) vũ trụ
歌手(kashu) ca sĩ
美人(bijin) mỹ nhân
安心(anshin) an tâm
安全(anzen) an toàn
古代 こだい（kodai） cổ đại（コーダイ）
注意 ちゅうい(chui) chú ý（チューイー）
留意 りゅうい(ryuui) lưu ý（ルウイー）
同意 どうい(doui) đồng ý（ドンイー）
悪意 あくい(akui) ác ý（アックイー）
意見 いけん(iken) ý kiến（イーキエン）
国歌 こっか(kokka) quốc ca（クオックカー）
愛国 あいこく(aikoku) ái quốc（アイクオック）
衣服 いふく(ifuku) y phục（イーフック）
管理 かんり(kanri) quản lý（クアンリー）
記念 きねん(kinen) kỷ niệm（キーニエム）
楽観 らっかん(rakkan) lạc quan（ラックアン）
観念 かんねん(kannen) quan niệm（クアンニエム）
天然 てんねん(tenen) thiên nhiên（ティエンニエン）
大路 だいろ(dairo) đại lộ（ダイロ）
暗殺 あんさつ(ansatsu) ám sát（アムサット）
観察 かんさつ(kansatsu) quan sát（クアンサット）
軍備 ぐんび(gunbi) quân bị（クアンビ）
改革 かいかく(kaikaku) cải cách（カイカック）
感動 かんどう(kandou) cảm động（カムドン）
独断 どくだん(dokudan) độc đoán（ドックドアン）
数 すう(suu) số (ソウ）
電気 でんき(denki) điện/điện cực
塗布 とふ(tofu) đậu hủ
語 ご (go) ngôn
国語 ごくご(gokugo) quốc ngôn
準備 じゅんび(juunbi) chuẩn bị
記憶 きおく(kioku) kí ức
国旗 こっき(kokki) quốc kì
変態(hentai) biến thái
回復(kaifuku) cải phục, khôi phục
動物(doubutsu) động vật
人物(jinbutsu) nhân vật
植物(shokubutsu) thực vật
失敗(shippai) thất bại
肛門(koumon) hậu môn
忍者(ninja) nhẫn giả
九尾(kuubi) cửu vĩ (From Naruto, nine tail fox)
日記(nikki) nhật ký
歴史(rekishi) lịch sử
多数(tasuu) đa số
大多数(daitasuu ）đại đa số
文化(bunka) văn hóa
文学(bungaku) văn học
中学(chugaku) trung học
小学(shougaku) tiểu học
大学(daigaku) đại học
学生(gakusei) học sinh
生服(seifukku) sinh phục
同服(doufukku) dồng phục
征服(seifukku) chinh phục
音（音読み:on/om, 訓読み:oto) âm, âm thanh
山 onyomi is “さん” san simialar to Sino-Vietnamese’s sơn, while its kunyomi is ”やま” yama
Same thing can apply to 火 南 北 童 西 水
But all and all, Vietnamese can enjoy Thai or Khmer or Chinese culture as much any foreign culture, and vice versa.