I have read in Wikipedia as well as other sources that continuous tenses are not formally recognized in Spanish as in English. Why is it excluded from being a tense? Is it true for other Latin (Italic) languages too?
Neither traditional Spanish grammar nor modern grammatical surveys of Spanish (by Spanish authors) recognize the existence of “progressive” or “continuous” tenses. As far as I know, neither do Portuguese, Italian or French.
In Spanish at least, the progressive constructions like estar + gerund are termed verbal periphrases (perífrasis verbales) and grouped with other common structures, like poder + infinitive, where a main verb in a non-finite form (infinitive, gerund or participle) is accompanied by a potentially inflected auxiliary. (Technically, the compound tenses are periphrases in this sense, but they are obviously deemed to be integrated enough in the conjugational paradigm that they are recognized as tenses.) The passive voice (ser + participle) is also considered a periphrasis, though it is often treated separately from the rest.
This is all in fact rather arbitrary, since Spanish “tenses” are a mixture of time, aspect and mood. There is no clear, logical reason why a progressive aspect shown by a periphrasis should not get a different tense. But that's how tradition works.
(One possible explanation might be that Spanish has a variety of progressive structures at its disposal: estar + gerund but also ir, venir, llevar + gerund, which are all variations with special nuances. That variety might dilute the idea of a single “progressive” tense.)
Yes, that's right. In Spanish grammar, names are given for the perfective tenses with haber (like "he comido" being the "pretérito perfecto" and so on) and for the passive voice ("ha sido comido" would be the "pretérito perfecto en voz pasiva"). But the combination "estar" + gerundio is never given a name. Expressions like "presente continuo" or "pretérito indefinido continuo", while occasionally seen and understood, are taken from English and are not traditional in Spanish descriptions of the language.
A possible reason is that the verb "estar" collocates with both the gerundio and the participio in Spanish ("estoy pagando la bebida", "la bebida está pagada") so it is simply considered as a productive use of the gerundio.
I think the situation is similar in the other Romance languages.