1. The primary purpose of Rashbam’s comment here is to oppose the famous midrash that claims the Israelites were forced to accept the Torah by God, who uprooted Mount Sinai, held it over the head of the Israelites and threatened to drop it on them if they failed to accept the Torah. In other words, the Israelites stood literally underneath (תחת) the mountain. (See e.g. Shabbat 88a, and Rashi ad Exodus 19:17.) More often, this midrash is connected to the verse in Exodus than to our verse, but a number of midrashic sources read the idea into our verse. See e.g. Song Rabba 8:1.

2. See also Rashbam’s commentary to Genesis 18:8, s.v. עומד עליהם.

3. Rashbam is now explaining the purpose of this piece of incidental information – that the Israelites were standing close to the bottom of the mountain. Following the midrashic reading that the Israelites were standing underneath the uprooted mountain, the phrase is clearly momentous and significant. But what is its significance if it only means that they were near the bottom of the mountain?
Rashbam’s answer is that the verse serves an anticipatory purpose: it prepares the reader for the Israelites’ expression of fear in 5:22. Since our verse tells us that the Israelites were very close to the bottom of the mountain and the mountain was on fire, we now will be able to understand their fear (5:22) that the fierce fire will consume them. Rashbam uses the phrase “had to be written” (הוצרך לכתוב), a standard phrase for him (and other exegetes) when introducing an anticipatory phrase.
See pp. 412 and 414 of Appendix I of my Genesis volume.