The reason has nothing to do with full-width characters, and everything to do with fonts.
For posts that don't contain moonrunes (i.e. CJK characters), the fontstack used for text in those posts is>arial,sans-serif
which basically means that your browser will display the post in Arial font, or some sans-serif font if your computer doesn't have Arial (almost every computer does though).
When a post contains a moonrune like >>3348
, a different fontstack is used, namely>ipamonapgothic,ipa モナー pゴシック,Mona,ms pgothic,ＭＳ Ｐゴシック,Osaka,YOzFontAA97,sans-serif
The ones in Japanese are just aliases of the English ones: ipa モナー pゴシック is the same as ipamonapgothic and ＭＳ Ｐゴシック is the same as ms pgothic
The fontstack is different because the Arial font you're using may not contain glyphs for every moonrune, i.e. the font may not have a picture of the character. When this happens, you see a rectangle instead where the character should be (this kind of problem comes up more often with emoji).
So you end up using a CJK-based fontstack, with fonts that can display CJK characters. On my computer, the first available font is MS PGothic, but on yours it looks like it might be ipamonapgothic instead. The HTML/CSS of the site applies this fontstack with post-granularity, so all the text in a post either uses one fontstack or the other.
Also the fonts used in the CJK-based fontstack aren't monospaced fonts, but proportional fonts, which is why there's a "p" in the font names. That just means the widths of characters are proportional to their sizes instead of being fixed like in monospace fonts.