In the answer to the thread What's the difference between 腹切{はらき}り and 切腹{せっぷく}? in the 1st paragraph, 2nd line, the author mentions "Sino-Japanese pronunciation and word order".
I assume that "Sino-Japanese pronunciation" is 音読{おんよ}み。
So, what is "Sino-Japanese word order"?
In this case, it's verb-object, like the Chinese these morphemes were borrowed from, rather than object-verb, like native Japanese syntax:
切腹 （せっぷく） ＝ 切（せつ） (verbal morpheme) + 腹 （ふく） (object morpheme)
腹切り（はらきり） ＝ 腹（はら） (object morpheme) + 切り（きり） (verbal morpheme)
Generally, the morphemes in Sino-Japanese compounds (called 漢語【かんご】 in Japanese) follow Chinese word order, even if those words were coined in Japanese rather than borrowed directly from Chinese.
Native Japanese compounds usually follow Japanese word order, except without particles:
腹を切る (verb phrase) → 腹切り (deverbal compound)
We can find other pairs like this, for example:
殺人 （さつじん） ＝ 殺（さつ） (verbal morpheme) + 人 （じん） (object morpheme)
人殺し（ひとごろし） ＝ 人（ひと） (object morpheme) + 殺し（ころし） (verbal morpheme)
And we can break down the latter like this:
人を殺す (verb phrase) → 人殺し (deverbal compound)
In fact, you can often "take apart" a Sino-Japanese compound by turning it around, switching to native Japanese readings (訓読み) and inserting the appropriate particles and such. If we use our example of 殺人 again:
殺人【さつじん】 → 人【ひと】を殺【ころ】すこと。
We just came up with the dictionary definition of 殺人 without actually looking it up.
The canonical word order in a Chinese sentence is SVO (subject-verb-object), while Japanese exhibits SOV (subject-object-verb) syntax. Sino-Japanese word order just refers to the appearance of Chinese word order in Sino-Japanese compounds.
Therefore 腹切り, which is a native compound, exhibits OV word order (being a nominalisation of 腹を切る), while the Chinese derived compound exhibits VO word order.
