Swami Vivekananda was a Sanyasi who had given up the worldly desires, for him a piece of meat or a portion of vegetables meant the same. For a true Sanyasi, you eat because body needs food, not because you like/enjoy the food.
Sanyasis are suppose to eat whatever is offered to them, and are not supposed to demand any kind of special food. So, while in USA and other foreign countries, Swami Vivekananda chose to eat whatever was offered by hosts, without making a fuss about it.
Please also note that, enlightened Yogis are trigunatit (beyond the Rajas, Tamas or Satvik), so these guna specific rules mentioned in Bhagavad Gita don’t apply to them.
BTW, If he would have been a pretend Sanyasi, who just wearing saffron clothes but hasn’t given up the worldly desires, then these rules would have applied. But he wasn’t like that, he was a true Sanyasi, an enlightened one, so what he did in terms of choice of food was ‘technically’ correct.
Having said that, as Krishna explained in Bhagavad Gita, the enlightened people, even though the rules don’t apply to them still should follow the rules, so that the normal people don’t get confused/mis-understood. In this context, I personally would have liked Swami Vivekananda choosing sativik part from whatever food is offered to him, that way normal people wouldn’t have used him as an example for eating rajasik/tamasik food.
As said earlier, None of the food choices swamiji made, impacted his spiritual progress, but they do impact spiritual progress of regular/normal people, by generating un-necessary karma. It’s responsibility of enlightened ones to help normal people stay on track.
BTW, this is one of the very few things where we don’t agree with Swami Vivekananda completely.