Why is Kabbolas Shabbos shortened on Shabbos Chol HaMoed / Shabbos Yom Tov?
The first five chapters of Tehillim (95-99) that we say at the beginning of Kabbalas Shabbos correspond to the first five days of the week. So when Yom Tov or Chol Hamoed coincides with Shabbos, it is inappropriate to say these "weekday-ish" chapters.
(Mizmor Ledavid, on the other hand, also represents a weekday, Friday - but that is a day of preparation for Shabbos, and so it is always suitable.)
Edited-Semi Transcript of this Shmuz By Rabbi Reisman:
(דוֹדִי לְכָה) is not a song about Shabbos alone. As a matter of fact, only the first 2 stanzas and the last stanza talk about Shabbos.The stanza of (אֶחָד בְּדִבּוּר וְזָכוֹר שָׁמוֹר) talks about Shabbos. (וְנֵלְֿכָה לְכוּ שַׁבָּת לִקְרַאת) talks about Shabbos, so we say them. The next stanzas talk about the Churban Beis Hamikdash and a desire for Mashiach to come. For example (מְלוּכָה עִיר מֶֽלֶךְ מִקְדַּשׁ) speaks about, you dwelled long enough in the valley of weeping. In other words we are talking about the fact that we want Mashiach to come. (קֽוּמִי מֵעָפָר יהִתְנַעֲרִ), Arise get up from your dust which is also talking about the desire of Klal Yisrael to come to its redemption (גְּאָלָהּ נַפְשִׁי אֶל קָרְבָה הַלַּחְמִי בֵּית יִשַׁי בֶּן יַד עַל). So too (הִתְעוֹרְֿרִי הִתְעוֹרְֿרִי) and (תֵבֽוֹשִׁי לאֹ) and (ךְשׁאֹסָֽיִ מְשִׁסָּהלִ וְהָיוּ). All of these talk about the Churban. Since they talk about a desire for the Geulah to come after the Churban so then when it is Yom Tov, a day of great Simcha we skip them. We say (וּשְׂמאֹל יָמִין) because that stanza envisions Mashiach coming and it doesn’t talk about the Tzaros of the Shibbud. However, the 5 that we do skip talk about the difficulties and therefore it is appropriate that we skip them on Yom Tov and that is the reason that we skip them. You may ask, indeed what is it doing here in (דוֹדִי לְכָה) in the first place? What are stanzas that talk about Churban and Geulah doing in (דוֹדִי לְכָה)? The answer to that is (דוֹדִי לְכָה) was written by the Mikubalim in Tzfas who came to Tzfas after the expulsion in Spain and they focused a lot on the hope and prayer that the expulsion from Spain would lead to Mashiach coming. When they sang (דוֹדִי לְכָה), you have all heard of the idea that they used to go out into the fields and greet Shabbos, greet the setting sun in the mountain tops which heralded the arrival of Shabbos. That greeting of Shabbos Malkisa was a M’ain of Mashiach’s times called the true Geulah. The real time of Yom Shekulo Shabbos was a day of a complete Shabbos. Therefore as they sang a song wishing and hoping for Mashiach to come, they mixed that with the song in which they mentioned their desire for the Kallah of Shabbos to arrive and the Tefilla that Mashiach would come.