Magento 2 : Show captcha at contact us form

In order to add CAPTHA to a Contact Us form you have to go to Stores -> Configuration -> Customers -> Customers Configuration page and Enable CAPTCHA. Make sure to select Contact Us value in Forms field.

Once you update configuration, clean cache.

Hope it helps.

You can make a custom form template (based on the original) then you can load reCaptcha block programmatically whith this :

<?php 
    echo $block->getLayout()
        ->createBlock('MSP\ReCaptcha\Block\Frontend\ReCaptcha',
            'msp-recaptcha',
            ['data' => 
                [
                    'jsLayout' => 
                    [
                        'components' => 
                        [
                            'msp-recaptcha' => 
                            [
                                'component' => 'MSP_ReCaptcha/js/reCaptcha',
                                'zone' => 'contact'
                            ]
                        ]
                    ]
                ]
            ]
        )
        ->setTemplate('MSP_ReCaptcha::msp_recaptcha.phtml')
        ->toHtml();
    ?>