Set the Render menu quality to Best. (In general, I have Dynamic turned off as well*.) I think when the template is used in FCPX, Best mode is automatic. You have more control over "render options" in Motion and Normal or Draft helps speed up playback while working. Changing the setting to best, you should see the text edges smooth out (as well as the bird detail).
Now, you can leave the settings at Normal (if you have the confidence) and when you go to Share/Export, you will be presented with a dialog:

You can set the Render Quality here if you like (notice how Use canvas setting is default on all of these options).
*I frequently change all these settings when I need to manipulate how Motion is rendering while I work, particularly in 3D Text because, when Dynamic is turned on, Motion frequently fails to immediately update ("real time") minor changes to Appearance parameters.. I'll frequently drop into draft mode if interaction is bogging down. Some "models" can get to be quite complex.
If you have problems running the template in Best Quality mode, consider reducing the original size down to 1620x1080 (you can even go a little smaller) in Preview. Open the image in Preview, go to the Tools menu, Adjust Size and there's a drop down menu labelled Fit Into — select 1920x1080 or 1280x720, then Export as a new PNG. The aspect ratio will not be distorted.
Not sure if this board will resize this upload, but I'll try (should be 1620x1080):

[Edit: yep -- image was resized by ASC to fit...
ASC Staff!! >> limiting image size like this makes screen captures VERY DIFFICULT to see. Please consider allowing full sized images, at least within the maximum upload limit.
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