Tense is a hard term to apply properly to English. We only inflect verbs (change the word itself) for person/plurality, perfect aspect, progressive aspect, and past (or preterite) tense.
When talking about grammar between languages, tense is one of the ways in which verbs change. It has to do with time. So, from that perspective, it is technically true to say we have three verb tenses - past, future, and present. However, most of the time these are marked with auxiliary verbs like will, did, have, or had. Only the past simple changes the verb itself.
Verb forms also have aspects, like progressive and perfect, and moods, like indicative, subjunctive and imperative. There's also the question of voice, being active or passive. In English, we inflect for progressive and perfect aspect, but not for anything else in that list. Mood and voice are indicated syntactically - by changing word order or adding or leaving out some words that might normally be used.
We don't usually use the term indefinite, but given what the slide says, I assume that they mean simple, which is the other aspect, the default aspect if you like. If so, then they have listed all the aspects/aspect combinations you can use - because sometimes a verb is both perfect and progressive, which is achieved by inflecting the verb itself for one, and the auxiliary verb for the other, adding another auxiliary along the way. So yes, you can make a three by two grid, one axis labelled "past, present, future" and the other labelled "simple, progressive, perfect, perfect progressive", and you get 12 different forms that verbs can take in English. However, it should be noted that the "present perfect" is a reference to the past, despite its name!
Yes, what they say is true, but it needs more explanation and has been put badly, and using terms that I would consider standard.