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I've found this Worldwide map or data for linguistic distance here when looking for a way to know if Portuguese is the most similar language to Spanish. Unfortunately neither of these languages are in the marked answer. Is it know through this mean or another, which language is the most similar to Spanish?

The map you have doesn't pass the sniff test for me. I don't imagine anyone realistically saying Catalonian being closer to Spanish than Galician. I can't speak for other Romance groups, but for Iberian languages, the chart on Wikipedia is in line with my experience (I speak Asturian, Castilian, and Portuguese, and regularly consume media in Galician and Aragonese).

The problem, however, when doing a lexical analysis is how you handle words that exist in both languages but have different frequencies of use, or with pronunciations that line up closer in one than another.

For example, cerrar (to close) exists in Portuguese, but fechar is used infinitely more. On the other hand, in both Asturian and Aragonese, the verb is zarrar. Which is closer? You can argue for Portuguese because cerrar is identical — but should the comparison really be with fechar which is more used and thus you could argue for Asturian or Aragonese with zarrar?

Or looking at Spanish’s despertar to Asturian's espertar, Portuguese and Catalan's despertar and Mirandese’s spertar which one is closer? Do we count them all the same since it's a direct etymological link and the only difference is the morphological form of *des ? How do we factor in Asturian's esconsoñar and Portuguese and Mirandese’s acordar? Do we link Asturian more closely because the two are about equally common in it but (de)spertar is rare in PT/MWL?

Do we let pronounciation factor in because some languages like Mirandese indicate vowels that would be spoken (but not written) in others like Portuguese? If you do, how do you decide which spoken variant to use? Gato in Portuguese/Mirandese is gato which might make them look closer to Spanish, but oftentimes the pronunciation will trend closer towards /u/ (Mirandese) or even silent (Portuguese) in which case … are they really closer to Spanish than Asturian’s gatu?

If you don't establish a clear methodology for how you're comparing things, then the numbers are meaningless. Most likely I would say that Ladino would be the language closest, but it has a modern writing system that probably obscures that closeness and I'm not familiar enough with it to say definitely. Otherwise, any of the West Iberian languages would be good candidates and I'm not sure you can say confidentally which one is lexically closer than the others for the reasons above.

If you read closely the map in the marked answer (not only the numbers displayed as text answer which focus only on Germanic languages), inside the part related to Italic-Romance languages, you'll notice it seems it is the Catalan language which is the closest to Spanish.

Galician and Portuguese seems to have the same distance with Spanish, but both are more distant than Catalan.

Besides, looking at the other answer, in the original map in Russian by Prof. Konstantin Tishchenko there is:

• Catalan completely next to Spanish,


• 
  Galician and Occitan/Provencal CLOSER to Spanish than Portugese

I have no clear idea about the validity and the methods used for the two maps.

An extremely rapid look skimming the answers mentions Levenstein distance, as a systematic method for computing the distance between two sentences. Maybe it is used on the same sentences translated in two languages. Check those answers more carefully for detailled informations. It is beyond my knowledge.

What the marked answer suggests, is that the author Prof. Konstantin Tishchenko used only a limited set of very usual words to calculate the Levenstein distance, or a simialr metric. If you look at the Swadesh list that could have been used, then you notice it is really short ! Only a hundred of words.

As stated in the comments related to your question: in which way South American Spanish, or even Mexicano or Boliviano or Chileno for instance, is considered another language ?

Namely, a clear example is Vos, a different person from Vosotros.
It is a person which is not used in Spanish (Castillano), isn't it ? This link explains when to use vos, compared to usted and tu in Chileno.

As a metaphor, it is a bit as if people of New-Zealand were using Thu (just invented, not related to reality), as a word that would have derived from Thou, to express informal singular You.