"Impossible to access an attribute on a NULL variable"
That message is telling you that gatewayHandle can't be accessed from video, because video is NULL. You're expecting the videos field to always contain an object, but in this case it is not.

I would suggest that you ensure that video actually contains a value before you attempt to reference one of its properties...

{% set video = entries.video %}

{% if video %}

    {% if video.gatewayHandle == 'youtube' %}
        ...
    {% endif %}

{% endif %}