It's not true, so not compelling. 73.2% of the world's greenhouse gas emissions are produced by energy production, agriculture is a drop in the bucket. Going vegan isn't going to change how you charge your iPhone.
Depending on your definition of "significant" one can argue about the emission part, but the interesting part of the cited claim surly is the landuse portion.
https://ourworldindata.org/emissions-by-sector