I was going to write this when the news about the murder first came out, but I think it needs saying now: Realpolitik was always going to win out in this case. Regardless of who the president was in this case, the US wasn't going to risk its relationship with a key strategic and economic partner over a single death of a non-national, regardless of how high profile this has become.
It's in the US' national interests to maintain a strong relationship with Saudi Arabia. And the US has historically not been above letting other countries get away with literal murder, or even conducting literal murder, if it supports their own geopolitical interests.
That said, Trump's handling of this has been simply appalling. Amateurish and petulant to boot. In local political terms, it just reinforces his willingness to cozy up to dictators and petty authoritarians while also making him look rather spineless. In international political terms, it shows the US as continuing to abdicate the mantle of moral responsibility that it has attempted to take on in global matters - worrying allies and weakening the country's international standing.
I'm not saying that Obama (or another candidate like Hillary or J Bush) would have done anything to threaten the US-Saudi relationship over this had it occurred during their administrations, but I'd bet a pretty penny that they would have handled the situation with a lot more care, tact and sense.