data:image/gif;base64 Images Not Animated
Your data does not consist of the entire original file. Using the data: URI Kitchen to encode the original image, we see the URI should instead be:
<img src='data:image/gif;base64,R0lGODlhyADIAPIFAP%2FyAAoKCgAAAcRiAO0cJAAAAAAAAAAAACH%2FC05FVFNDQVBFMi4wAwEAAAAh%2BQQJCgAFACwAAAAAyADIAAAD%2F1i63P4wykmrvTjrzbv%2FYCiOZGmeaKqubOu%2BcCzPdG3feK7vfO%2F%2FwKBwSCwaj8ikcslsOp%2FQqHRKrVqv2Kx2y%2B16v%2BCweEwum8%2FotHrNbrvf8Lh8Tq%2Fb7%2Fi8fs%2Fv%2B%2F%2BAgYKDhIWGh4iJiouMjY6PkJGSk5SVlpeYmZqbnJ2en6ChoqOkpaanqKmqq6ytrq%2BwsbKztLW2t7i5uru8vb6%2FwMHCw8TFxsfIycrLzM3Oz9DR0tPU1dbX2Nna29zd3t%2Fg4eLj5OXmkwLpAszq68vt7OrI7QH1AfDD9Pb4wvr1%2FMH83ZP3S6C9gemAGdxH0NfCfw17PUTozqG6gwcBkph4EP%2FSRI0jONrzeBEjxIQnRNYjmc7kyYolVAZgKcAlRRDt2gHYybPnzo6PPkbkkFOdz6MAgDoSitJD0XRIfSptxBQm0adRe05lpBMpSAtds2bduiisz68VzIo9SlaRWp5oKbxdy7NtorkA4k7AS9cumKeAA9vMiNXr0L1G6a71%2ByWw45yDGRaNqtcBX8U%2FR555zLlmZIp4Kze4jJmxl86PP4NOfFQ0A9KKTWeReRCzbcNNI8C%2BLRsLbXu3g8M9bJm1cKS9r%2Fyudzy46N22k1tZHqD57efGrdfVbEamVuDazxIvAF249NklI39nHr4n2vLBz%2FtOP3h99fbDc7%2FOjj%2Fzys3%2F9NlkX387vcdff%2FJtgVpL4PVnIFTHqQbHgp6x5%2BB48Nln04QL1kbggwI0J%2BEbFHp4oX4LZLhdZICYiJ9sZg0g4wD2MeJiezAaNyONK860yI3h5QjhTjvW%2BGODL3Knm44zGqmIi6EdmJSSELSz45UzJqgHlFLiJaQAWGKpZR5cDimemU4umU6YV46JR5kh4hYnW1Q%2BYCWbWdZpyEEE9EnAbX7%2B2SOFd4qpZyF8%2BgmoooMSumaYbt6RaJ%2BLUtqoo2xGasekgmIWqH2OPmrof44AqV2RPKEqlqZ9mGqdqgDAGhWrfLjaHKyyIneojUi2h2uTi%2B36iGq3%2FSpjX8KW%2Blmxh8AS2exYyTZCrG3G8rhqtLyqR%2B2zudJJaie2EpgmJ%2BGK65%2BPnpRrLq2HqCsuu3v2aq636IIr77zjbuIugfAiei%2B%2B54LiooA9DuxSvpoYbJKGSBIc8CcKY8SwhVMu3KPADR9ccMYWPyyKXSAf6pq%2Bh4b87X4oflzyyienOB7GLStgcr0oW%2FVEAgAh%2BQQJCgAFACwsAHwAbABMAAAD%2F1i63P4wPkGFvDjrzXO1XSiOJPSVaKpK5%2Bq%2B4RfMQQvfOCPTdu6%2Fu1nvR0QFa5WiUnSkISnL6KbJS0qvrIrTOcR6FVSh9UsuhJ%2Bg29n5PXdXa1pbuxVDcfHZnFK3p2F5AXsCfWgpHx8AiouMimxebmMkiBWNlgCPWJF3JZQUl42ZV5t%2FI54CoIyiUomXbx6VqbKrUa2Wrxi2spe0S7qMuBe%2Fu6pykLG3khzDxI7GYKfRlIVcnqDBDszNxXoL0t901Gja2A3a287d0ODS4n7kysLI6Jai7N%2Fu4%2FPA8Vmf9Lyq8MlHA6BBAOXOHaw2kGCAgwAT7oO4iCEhhw8pbpP4T%2F8jNzQYM3rcxRHVyIrPzISj9vHkolcKNdpbWailS4T9VHa8mU6QN5p9bLqEOdHlzIYsUc7gSXQnz1462TlhmjNmqny57l1cerOpSYNY5d2b2rVq0WZh%2FUktWJaTubPE0qogazSliXkD8g74KIXuSag68OrlG8XvSMA%2Fd%2Brdq9TnEsMeEa%2F7CmAx4cdsFcFz2jgrhcWg9UqG4Xcz5csRPoQOPfpF6bPaRqtevbi1i9ecNZ%2BVXYF2bbtEnBAYToAe8eKNtSKibXuFcOLGoSdX3nt187k0jkcf%2FpF6ddbAfzznjk77dO%2FMwyuBrNHyIvez1PfNfBJ%2B5cG7rudgT9G%2BfVCl%2BuHAH0T%2B4RefOmUskA89BeYVl3xeLIhOg4wd6FiCCki4DYUPIoihhs1wmB%2BEGGZIH08AkljigCj2VOIFLLYYIBYxojjjFTU%2BpeKHJ7YYyo4J5njTjfNx5WNAHr7YgF81NcZkUJ0pCcGTdXxE5RaoScnAlVzS16SLWjrQpZGYQNnTlWFKANWa6pWTZgFsJmminFG9iUGcF27ZZk52Kqgenne5NUICACH5BAUKAAUALDAAfABsAEwAAAP%2FWLrc%2FjA%2BQYW8OOvNc7VdKI4k9JVoqkrn6r7hF8xBC984I9N27r%2B7We9HRAVrlaJSdKQhKcvopslLSq%2BsitM5xHoVVKH1Sy6En6Db2fk9d1drWlu7FUNx8dmcUrenYXkBewJ9aCkfHwCKi4yKbF5uYySIFY2WAI9YkXcllBSXjZlXm38jngKgjKJSiZdvHpWpsqtRrZavGLayl7RLuoy4F7%2B7qnKQsbeSHMPEjsZgp9GUhVyeoMEOzM3FegvS33TUaNrYDdrbzt3Q4NLifuTKwsjolqLs3%2B7j88DxWZ%2F0vKrwyUcDoEEA5c4drDaQYICDABPug7iIISGHDyluk%2FhP%2FyM3NBgzetzFEdXIis%2FMhKP28eSiVwo12ltZqKVLhP1UdryZTpA3mn1suoQ50eXMhixRzuBJdCfPXjrZOWGaM2aqfLnuXVx6s6lJg1jl3ZvatWrRZmH9SS1YlpO5s8TSqiBrNKWJeQPyDvgohe5JqDrw6uUbxe9IwD936t2r1OcSwx4Rr%2FsKYDHhx2wVwXPaOCuFxaD1SobhdzPlyxE%2BhA49%2BkXps9pGq169uLWL15w1n5VdgXZtu0ScEBhOgB7x4o21IqJte4Vw4sahJ1fee3XzuTSORx%2F%2BkXp11sB%2FPOeOTvt078zDK4Gs0fIi97PU9818En7lwbuu52BP0b59UKX64cAfRP7hF586ZSyQDz0F5hWXfF4siE6DjB3oWIIKSLgNhQ8iiKGGzXCYH4QYZkgfTwCSWOKAKPZU4gUsthggFjGiOOMVNT6l4ocnthjKjgnmeNON83HlY0AevtiAXzU1xmRQnSkJwZN1fETlFqhJycCVXNLXpItaOtClkZhA2dOVYUoA1ZrqlZNmAWwmaaKcUb2JQZwXbtlmTnYqqB6ed7k1QgIAOw%3D%3D' />
Which does indeed animate.
Your base64 encoded data isn't animated gif. I encoded the original image that you linked and it works fine.
<img src='data:image/gif;base64,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' />
Fiddle