They absolutely have been the main force behind the timing of this push. It was the main topic of General Conference a few weeks ago and one of the most eyebrow-raising articulations of official church policy.

Given the way that the church has explicitly encouraged state legislators to shoot down recent laws it's not surprising to think they'd be pushing for this.

I thought it worth posting the stance for those not willing to click

... Gambling is motivated by a desire to get something for nothing. This desire is spiritually destructive. It leads participants away from the Savior’s teachings of love and service and toward the selfishness of the adversary. It undermines the virtues of work and thrift and the desire to give honest effort in all we do.

Those who participate in gambling soon discover the deception in the idea that they can give little or nothing and receive something of value in return. They find that they give up large amounts of money, their own honor, and the respect of family members and friends. Deceived and addicted, they often gamble with funds they should use for other purposes, such as meeting the basic needs of their families. Gamblers sometimes become so enslaved and so desperate to pay gambling debts that they turn to stealing, giving up their own good name.

Also "Utah is one of only two states where gambling is also prohibited under the state constitution"

Ehh I wouldn't try to appeal too much to what the LDS church thinks about this. They require members to give 10% of their annual income to the church, while already having close to $300 billion in the bank.

Everyone knows the state of Utah is largely run by the church.