Since OP asked me in another thread to post this here, I'll start with what I think of the sound used by the native speaker in the video.
The Italian word "tagliatelle" pronounced by native Italian speakers sounds to the Japanese like タリアテッレ, タリアテーレ, タリアッテレ or something along those lines (or it does at least to me). So I'm guessing that the Japanese guy in the video is simply mimicking the Italian sound within the Japanese phonology. So, his /r/ there may not be representative of natural Japanese.
In any case, if it is a trilled /r/, I guess you can analyze the /rure/ part as one "syllable" /rre/, i.e., it contains a trilled /r/ with some sort of gemination. But as a native Japanese speaker, I'd say it's just two moras ルレ said quickly. At least my brain hears it that way, regardless of how the sound is being realized by his mouth.
Also, usually it's not difficult to realize a geminated version of a phoneme like /r/ in a given phonetic/phonological context. If it is a consonant that is not usually geminated in Japanese (as in a loanword like this case), you just come up with an analogous 促音 sound on the fly so it flows best. You can even make a 促音 at the end of a sentence, where there's literally no sound to stretch out. The mechanism is explained here in the Japanese Wikipedia article on 促音.
In your case, if a Japanese person who has never heard タリアテッレ (or tagliatelle) in their life is to pronounce it as a loanword they just ran into (e.g., it's written on a menu this way in katakana), it'd be something along the line of
レ (← This final mora is lower in pitch than タ.)
with the required pitch drop at レ for pitch accent and gemination on /r/ the same way as you'd do on some other phoneme. I'm pretty sure the vast majority of the native Japanese speakers understand what タリアテッレ (テにアクセント) should sound like, although there can be variations. Personally, I seem to realize 促音 for this particular word (in this kana spelling) by the following method explained in the Wikipedia article:
So, what I'd do is basically to first make a glottal stop while placing my tongue in the regular /r/ position), hold it by one mora, and then realize /r/ in the normal way. Probably this can depend on other factors like how quickly I pronounce it. But with this pitch pattern (which I think is the natural choice for many native speakers), I seem to use the glottal stoppy version.
Edit: I can't seem to correctly align the kana above in the pitch accent description; the preview looks fine, but when it's posted, stachexchange renders it differently than what I'm seeing in my preview... Anyway, レ at the end should be lower than タ if said in isolation.