Interrupting $html.= ‘ for IF statement

This is more general PHP than anything WordPress specific.

String concatenation occurs whenever you combining two stings with the . operator. During string concatenation some basic PHP keywords will not apply and you’ll need to use the shorthand equivalent instead. In this case you can use the ternary (conditional) operator

$html.= '<span class="cat">In '. ( $terms_string === "Articles" ) ? 'glyph HTML code' : '' .' <a href="'. $typeLink . '">' . $terms_string . '</a></span>';

A better, more readable format may be breaking up the HTML output into multiple strings:

$html.= '<span class="cat">In ';

if( "Articles" == $terms_string ) {
    $html .= 'glyph HTML code';
}

$html .= '<a href="'. $typeLink . '">' . $terms_string . '</a></span>';