Вам необходимо добавить в файл TS свойство, чтобы показать скрыть
navbarCollapsed = true;
toggleNavbarCollapsing() {
this.navbarCollapsed = !this.navbarCollapsed;
}
Обновить использование HTML (click) = "toggleNavbarCollapsing ()
<nav class="navbar navbar-inverse navbar-static-top">
<div class="container-fluid">
<div class="navbar-header">
<a routerLink="home" class="nav-link" routerLinkActive="active" class="navbar-brand"><img src="../../assets/img/logo.png" class="img-responsive logo" alt=""></a>
<button type="button" class="navbar-toggle collapsed" (click)="toggleNavbarCollapsing()" data-toggle="collapse" data-target="collapseMenu" aria-expanded="false" aria-controls="navbar">
<span class="sr-only">Toggle navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
</div>
<div id="collapseMenu" class=" collapse navbar-collapse" [class.collapse]="navbarCollapsed">
<ul class="nav navbar-nav navbar-left">
<li><a routerLink="games" class="nav-link" routerLinkActive="active">Games</a></li>
</ul>
</div>
</div>
</nav>
Демо: https://stackblitz.com/edit/angular-bootstrap3-toggle