OLAP is characterized by fairly low-volume aggregation queries that touch very large volumes of data ("what fraction of tweets in English come from non-english speaking countries?"). Sure, the ingest is large, but it tends to be batch and has fairly loose real-time (in the EE sense) requirements. What makes OLAP hard is the sheer volume of data from which an aggregation must be calculated.
OLTP is characterized by very selective queries with much tighter real-time bounds ("what are the last 20 things that the 100 people I follow said?"). The overall size of the dataset might even be the same, but each individual query needs fast access to a tiny fraction of the dataset. In many applications, this is accompanied by very high QPS and in Twitter's case, extremely high write volume.