\documentclass[a4paper]{memoir}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[danish]{babel}
\usepackage{amsmath,amssymb,mathtools,bm,url,amsthm}
\usepackage{lipsum}
\theoremstyle{definition}
\newtheorem{videox}{Video}[chapter]
\makeatletter
\newenvironment{video}[1]{%
\begin{videox}
test
\@afterindentfalse
\@afterheading
\par
}{\end{videox}}
\makeatother
\begin{document}
\setcounter{chapter}{3}
\lipsum[4]
\begin{video}{vid:a2}
\end{video}
\lipsum[4]
\begin{video}{vid:a3}