If the first agent could be shown as having "abandoned" the buyers (he never showed up) and the second agent picked them up and ensured the sale
In our jurisdiction, that would be called intrusion. Some or all commissions, fines, and licensing penalties applicable.
The prospective purchasers arrived at the property, arranged by Agent #1. At some point they decided to converse with Agent #2. Was the prearranged meeting not disclosed. Did Agent #2 not suspect or outright query such?.
Agent #1's timeliness may have not been impressive, but certainly not abandonment (again referring to my jurisdiction it is 10 days non contact). A hearing would certainly divulge his justifications.
On the other hand, Agent 2, although we are not told, should have suspected something was amiss (how could the prospects not have projected this?). Although not required, he likely should have suggested that these prospects call the realtor to help them get back on track. And on this particular property, he should not have made himself available if he became aware of the situation. He exposes himself to penalty if he uses derogitory indicators towards Agent 1.
All said and done, if the prospects move on the original property with Agent 2, this Agent should seek advice from his broker because he could be heading for a hearing.
I the prospects called and spoke with Agent 1 and his broker, declaring their dissatisfaction and that they are dropping him over Agent 2, that may satisfy the 'intrusion' issue, but that still may not stop Agent 1 from filling complaint along with compensation against Agent 2.
To the purchasers it should make no difference with what may have been a mix up on where to meet first. I sounds awful suspicious that Agent 2 had a few things to say about Agent 1.
So to make a long story short, and specifically reply to the original query, if it was in our jurisdiction, NO, you do not have to go with anyone specific agent, unless you have a written buyers agreement. The agent you use however, operates under a number of rules and regulations, and may be penalized if he contravienes any of these.