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There's no "official" requirement for what you describe. The relevant point is where the injured player was being attended to, rather than who was attending to him. If he was in any way near enough to the field of play when he was being attended to be in danger, delaying the game until it was safe for him and his attendees would be appropriate.
However, if his proximity to the field did not pose any potential risk, there is no reason for delay. The fact that the Head Coach chose to stay with the injured player rather than focus on his team's try activities is totally irrelevant. That's why each team has trainers and medical personnel in attendance and why there are assistant coaches.
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