Your opinion is sound. The statement is connected to the present.
The complete verb of the clause in question is "has given". The "has" uses the present tense. The "given" uses the perfect aspect.
The meaning of the present tense is obvious. This verb has a location in time, and that location is now.
The meaning of the perfect aspect might be less obvious. The word "perfect" means something like "complete" or "finished". In this sentence, that meaning makes sense. The act of giving is complete.
The FAA gave the go-ahead. That action is finished. The city now has the go-ahead. This state-of-being exists in the present. The verb form "has given" represents the present-tense result of that finished act of giving.
Ordinarily, the finished action is an action in the past. This is the reason that the name for the perfect aspect form is "the past participle". However, past participles do not have a tense. This can be demonstrated by listing past, present and future tense verb constructions, all using the perfect aspect: had given, has given, will have given. It is even possible for the perfect aspect to be unfinished, incomplete, or ongoing. This can be demonstrated by listing verb constructions that also include the continuous aspect: had been giving, has been giving, will have been giving.
What the perfect aspect always does is indicate a relevant result.
In the sentence in question, the relevant result is that one Texas city has the go-ahead given by the FAA. In other words, that city has the authorization to being building a commercial space port.