Is there any workaround how to do \dddot even with Katex?

\stackrel{\cdot\cdot\cdot}{x} is not a terrible reproduction.
You can define this as a macro via {macros: {"\\dddot": "\\stackrel{\\cdot\\cdot\\cdot}{#1}"}}.

Maybe a better version is \stackrel{\raisebox{-0.2ex}{$\scriptsize\cdot\cdot\cdot$}}{x}.
Macro version: {macros: {"\\dddot": "\\stackrel{\\raisebox{-0.2ex}{$\\scriptsize\\cdot\\cdot\\cdot}}{#1}"}}

Reading AMSTeX's definition of \dddot:

\def\dddot#1{{\mathop{#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@
 \hbox{\normalfont ...}\vss}}}}

a maybe closer reproduction in KaTeX is \mathop{x}\limits^{\hbox{\normalsize ...}}
Or {macros: {"\\dddot": "\\mathop{#1}\\limits^{\\hbox{\normalsize ...}}"}}

But KaTeX seems to do the italic correction incorrectly, so this doesn't look great with e.g. A. Possibly related to #1821.

Oh, I just realized that the vertical alignment is off in all of these macros, so maybe they are not great. ☹️

One more version that fixes the vertical alignment (but still has the italic correction issue):

{\overset{\raisebox{-0.1ex}{\normalsize ...}}{x}}"
{macros: {"\\dddot": "{\\overset{\\raisebox{-0.1ex}{\\normalsize ...}}{#1}}"}}

Pretty close to LaTeX's rendering:

This seems close enough that I'll work it into a PR.