Shulchan Aruch (OC 65) says to say "Sh'ma" with the congregation when they say it, and Mishna B'rura 9 there says the same is true of other things recited as a congregation such as "Ashre" and "Alenu". (Indeed, it is common practice that one recites "Alenu" when the congregation does even if he is not at that point in the service or is not praying at all.) In what sense are the latter two considered prayers that are recited communally (more so than most of the rest of the prayer service), that the Mishna B'rura mentions them as communally-recited prayers? That is, what makes them communal, whereas other prayers aren't necessarily so considered?
Regarding Ashrei see one of the answers to this question. He cites Ramba"m and, more importantly Talmud Brachot which states that the beginning words refer "to those who dwell in your house". This is a reference to those that come to the Bet Midrash and to shuls. The Gemarah states that people would spend time meditating in the shul prior to the start of davening. Ramba"m clarifies the requirements moreso stating rules about if the Chazan stands or sits and what the congregation does. So, this definitely seems like a communal prayer.
Aleinu is something I have to investigate further. But, offhand, the language is in plural, esp. the 1st word, so it appears to have communal context. Also, note that that the history of Aleinu originally had it as part of the Yom Kippur avodah service which was communal. B"N, I'll research more and edit this.