I suspect that you’ve hard coded the 10.5/13.5 font and lead in points rather than pixels. Kindle does not like this. It sees the world in pixels. Further, you’re better off coding things in terms of ems.
Kindle “look inside” is essentially Kindle’s cloud reader, so the features are very limited. I suspect that the 10.5 value, rather than a whole number is confusing the heck out of the rendering engine. (Kindle doesn’t like fractions, either.)
The font size at 10.5pt is WAY too small for a kindle, which sees things in pixels. The rule of thumb is that the default size is 16px – which may be relative to the screen resolution of the device, or converted in some other way. However, if you go with 1em = 16px, you should be able to figure out the proportional math from there. You can use fractions with ems: e.g., .5em, .75em, are perfectly acceptable.
WRT Kindle Cloud reader: Again – very limited functionality here. I’m not even sure where the Kindle Cloud reader pulls the TOC from (the nav.xhtml or the NCX – I know it’s the nav.xhtml for KF8 supporting apps and devices. I do not know the last time Kindle Cloud reader was updated, and therefore do not know how limited the support for KF8 may or may not be).
Make sure that you have a nav.xhtml file in addition to the NCX and try again. This may be the missing “magic smoke” to your TOC problem.
Hope this helps.
Best regards,
Jean