To my ear, the native Japanese speaker in the video sounds like saying /tariatterure/ with the typical Japanese gemination occurring on /t/ and only on this consonant. So, I focus on when trilled /r/ might typically appear in Japanese, and post my impression on the /r/ in the video in question to here, which OP suggested.
If you're referring to the kind of allophone on /r/ that typically appears in yakuza speech, as you said yourself, it is called 巻き舌 (まきじた) in Japanese. Phonetically speaking, it's the alveolar trill.
This is not one of the allophones the average native Japanese speaker would use when speaking in standard Japanese in normal context. As the Japanese Wikipedia article on the alveolar trill says, this allophone is most typically associated with the dialects(?) called べらんめえ調 spoken by 江戸っ子 (えどっこ) and 浜言葉 typically stereotyped as fishermen's speech, and a certain aggressive, hostile, and rough register in spoken language (such as typical yakuza speech).
I'm not sure if it's linguistically true that this sound is regularly used as a major variant of phoneme /r/ in any of the alleged dialects/register. But as a native Japanese speaker, I do understand these "stereotypes." In fact, as is exemplified in the other video you linked to in the comment, the stereotypes are so widespread that this trilled /r/ (or its connotations to a rough, aggressive or rude manner) can be effectively exploited in fiction. You may also use it to sound humorous just like any other stereotypical speech. So, at least it's "widespread" in a sense and is definitely part of the Japanese language. But as far as I know, it does not appear as a regularly used (free) allophone in any of the major dialects I know or speak. Then again, I wouldn't be terribly surprised if someone uses it very often in a regular manner as part of their natural idiolect, either.
In any case, the examples I can be sure about are the three I mentioned above, i.e., べらんめえ調, 浜言葉, and yakuza speech, all of which sound "rough." Note that while べらんめえ調 is informally said to be the same as 江戸言葉, which is one of the regional dialects in Tokyo, the Wikipedia article of this dialect doesn't mention trilled /r/. So, it's possible that 江戸言葉 as the real regional dialect (which is becoming quite obsolete nowadays by the way) doesn't have this allophone, so perhaps it's just a stereotype thing.
