Impossible to access an attribute (title) on a string variable
entryCategory is already a single category because of "first()". So no need for the for loop. Just {{ entryCategory.title }} should do the trick here.

{% set entryCategory = entry.videoCategory.first() %}
{% if entryCategory %}
    &lt;h1&gt;&lt;a href=""&gt;{{ entryCategory.title }}&lt;/a&gt;&lt;/h1&gt;
{% endif %}