Help replicating this Document Design

With tikzpagenodes you can adjust things to the width of the actual page. It has the node current page text area, which is a rectangle that covers the text area.

\documentclass[twoside]{scrbook}
\usepackage[letterpaper, left=1.5cm, right=1.5cm, bindingoffset=1.5cm]{geometry}
\usepackage[utf8]{inputenc}
\usepackage{fancyhdr}
\usepackage{titlesec}
\usepackage{tikzpagenodes}
\usepackage{lipsum}
\usepackage{etoolbox}
\patchcmd{\chapter}{\thispagestyle{plain}}{\thispagestyle{fancy}}{}{}

\definecolor{gmitblue}{RGB}{93,138,168}
\definecolor{midnightgreen}{rgb}{0.0, 0.29, 0.33}

\usetikzlibrary{calc}
\renewcommand{\headrulewidth}{0pt}

\pagestyle{fancy}
\fancyhf{}
\fancyhead[CO]{%
\begin{tikzpicture}[overlay, remember picture]%
\fill[midnightgreen] ($(current page.north west)+(0.25in,-0.35in)$) rectangle ($(current page.north west)+(0.65in,-0.75in)$)
node[midway,text=white, font=\large\bfseries] {\thepage};
\fill[midnightgreen] ([yshift=-0.35in]current page.north-|current page text area.west)
coordinate (TL)
rectangle ([yshift=-0.75in]current page.north-|current page text area.east);
\node[anchor=north west, text=white, font=\large\bfseries,text
height=0.2in,inner xsep=1em] at (TL) {\rightmark}; 
\end{tikzpicture}%
}
\fancyhead[CE]{%
\begin{tikzpicture}[overlay, remember picture]%
\fill[midnightgreen] ($(current page.north east)+(-0.65in,-0.35in)$) rectangle ($(current page.north east)+(-0.25in,-0.75in)$)
node[midway,text=white, font=\large\bfseries] {\thepage};
\fill[midnightgreen] ([yshift=-0.35in]current page.north-|current page text area.west)
coordinate (TL)
rectangle ([yshift=-0.75in]current page.north-|current page text area.east);
\node[anchor=north west, text=white, font=\large\bfseries,text height=0.2in,inner xsep=1em] 
at (TL) {\leftmark};
\end{tikzpicture}%
}
\setlength{\headheight}{12pt}

\title{A reasonably long title}
\date{\today}
\author{The author}

\begin{document}
\maketitle
\chapter[Hola Mundo]{Hola Mundo}
\lipsum[1-9]
\section{La prueba na' ma'}

\chapter[Hola de Nuevo]{Hola Mundo\dots\space de Nuevo}
\lipsum[10-29]
\end{document}

Based on the code of @marmot, I added some missing parts. Please see the MWE later.

To recreate the shown structure of a document you need to add some code to your given MWE:

1. Add \usepackage{multicol} in your preamble and then add the following code to get a TOC in two columns:

   \begin{multicols}{2} % <================================================
   \tableofcontents % <====================================================
   \end{multicols} % <===================================================== 
   

2. I added \maketitle to your code to get the title of the document.

3. To be able to add easily an complete dummy document I changed \usepackage{lipsum} to

   \usepackage{blindtext} % <========================== \Blinddocument
   

   Remember to change \lipsum... to \blindtext ...

4. To get your wanted header on chapter pages etc., too, you have to define

   \fancypagestyle{plain}{% <==============================================
   

   (see the full code in the following MWE).

5. Please see that I added at the end of your text \Blinddocument to get a better filled TOC for showing the two column TOC.
6. Have you noticed the warnings you got because you are using a KOMA-Script class with fancyhdr and titlesec? KOMA-Script has an own way to build headers with package scrlayer-scrpage (please see documentation with texdoc KOMA-Script on your terminal/console). You should consider to change to that package but that was not the question here (If you can not do it by your own, ask a new question and show what you have tried so far ...).

The complete corrected MWE:

\documentclass[twoside,letterpaper]{scrbook}

\usepackage[letterpaper, left=1.5cm, right=1.5cm, bindingoffset=1.5cm]{geometry}
\usepackage[utf8]{inputenc}

\usepackage{fancyhdr} % <=========================== better use scrlayer-scrpage
\usepackage{titlesec} % <=========================== see warnings in log file
\usepackage{multicol} % <===============================================
%\usepackage{tikz}
\usepackage{tikzpagenodes}
\usetikzlibrary{calc}
\usepackage{blindtext} % <========================== \Blinddocument

\usepackage{etoolbox}
\patchcmd{\chapter}{\thispagestyle{plain}}{\thispagestyle{fancy}}{}{}

\definecolor{gmitblue}{RGB}{93,138,168}
\definecolor{midnightgreen}{rgb}{0.0, 0.29, 0.33}

\usetikzlibrary{calc}
\renewcommand{\headrulewidth}{0pt}

\pagestyle{fancy}
\fancyhf{}
\fancyhead[CO]{%
\begin{tikzpicture}[overlay, remember picture]%
\fill[midnightgreen] ($(current page.north west)+(0.25in,-0.35in)$) rectangle ($(current page.north west)+(0.65in,-0.75in)$)
node[midway,text=white, font=\large\bfseries] {\thepage};
\fill[midnightgreen] ([yshift=-0.35in]current page.north-|current page text area.west)
coordinate (TL)
rectangle ([yshift=-0.75in]current page.north-|current page text area.east);
\node[anchor=north west, text=white, font=\large\bfseries,text
height=0.2in,inner xsep=1em] at (TL) {\rightmark}; 
\end{tikzpicture}%
}
\fancyhead[CE]{%
\begin{tikzpicture}[overlay, remember picture]%
\fill[midnightgreen] ($(current page.north east)+(-0.65in,-0.35in)$) rectangle ($(current page.north east)+(-0.25in,-0.75in)$)
node[midway,text=white, font=\large\bfseries] {\thepage};
\fill[midnightgreen] ([yshift=-0.35in]current page.north-|current page text area.west)
coordinate (TL)
rectangle ([yshift=-0.75in]current page.north-|current page text area.east);
\node[anchor=north west, text=white, font=\large\bfseries,text height=0.2in,inner xsep=1em] 
at (TL) {\leftmark};
\end{tikzpicture}%
}

\fancypagestyle{plain}{% <==============================================
\fancyhf{}
\fancyhead[CO]{%
\begin{tikzpicture}[overlay, remember picture]%
\fill[midnightgreen] ($(current page.north west)+(0.25in,-0.35in)$) rectangle ($(current page.north west)+(0.65in,-0.75in)$)
node[midway,text=white, font=\large\bfseries] {\thepage};
\fill[midnightgreen] ([yshift=-0.35in]current page.north-|current page text area.west)
coordinate (TL)
rectangle ([yshift=-0.75in]current page.north-|current page text area.east);
\node[anchor=north west, text=white, font=\large\bfseries,text
height=0.2in,inner xsep=1em] at (TL) {\rightmark}; 
\end{tikzpicture}%
}
\fancyhead[CE]{%
\begin{tikzpicture}[overlay, remember picture]%
\fill[midnightgreen] ($(current page.north east)+(-0.65in,-0.35in)$) rectangle ($(current page.north east)+(-0.25in,-0.75in)$)
node[midway,text=white, font=\large\bfseries] {\thepage};
\fill[midnightgreen] ([yshift=-0.35in]current page.north-|current page text area.west)
coordinate (TL)
rectangle ([yshift=-0.75in]current page.north-|current page text area.east);
\node[anchor=north west, text=white, font=\large\bfseries,text height=0.2in,inner xsep=1em] 
at (TL) {\leftmark};
\end{tikzpicture}%
}}
\setlength{\headheight}{14pt}

\title{A reasonably long title}
\date{\today}
\author{The author}


\begin{document}

\maketitle % <==========================================================
\begin{multicols}{2} % <================================================
\tableofcontents % <====================================================
\end{multicols} % <=====================================================
\chapter[Hola Mundo]{Hola Mundo}
\blindtext
\section{La prueba na' ma'}

\chapter[Hola de Nuevo]{Hola Mundo... de Nuevo}
\blindtext

\Blinddocument % <======================================================
\end{document}

and its result:

and an usual chapter page: