Yep! Tamago is egg. Yaki is from the verb yaku which means grill in this context. Teri I didn't know, but it is the kanji from verbs that have to do with shining so probably refers to the glaze being shiny.
Use a high gluten rice in the filling, and chill the burrito in a sealed container for a couple hours. The condensation from chilling helps the tortilla stay slightly tacky so it will stick to itself, and at the same time it thickens the oils to help promote cohesion. After that it's just a matter of being really gentle, having a very very sharp knife, and cooking it at high temps on just one side.